Advances in chromatography, volume 50 1439858446, 9781439858448, 1439858454, 9781439858455

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Volume

50

EDITORS

Eli Grushka • Nelu Grinberg

Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an informa business

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CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2012 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Version Date: 20110826 International Standard Book Number-13: 978-1-4398-5845-5 (eBook - PDF) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information storage or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com

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Contents Foreword.....................................................................................................................v Contributors..............................................................................................................vii Chapter 1 Mixed Beds........................................................................................... 1 Egisto Boschetti and Pier Giorgio Righetti Chapter 2 Mechanistic Studies of Chiral Discrimination in Polysaccharide Phases......................................................................... 47 Hung-Wei Tsui, Rahul B. Kasat, Elias I. Franses, and Nien-Hwa Linda Wang Chapter 3 Chromatographic Separation and NMR............................................. 93 Nina C. Gonnella Chapter 4 Principles of Online Comprehensive Multidimensional Liquid Chromatography.................................................................... 139 Peter W. Carr, Joe M. Davis, Sarah C. Rutan, and Dwight R. Stoll Chapter 5 Organic Monolith Column Technology for Capillary Liquid Chromatography................................................................................ 237 Yuanyuan Li, Pankaj Aggarwal, H. Dennis Tolley, and Milton L. Lee Chapter 6 A Brief History of Superficially Porous Particles............................. 281 Joseph J. DeStefano and Joseph J. Kirkland Chapter 7 The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity............................................................................ 297 Lloyd R. Snyder, John W. Dolan, Daniel H. Marchand, and Peter W. Carr

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Contents

Chapter 8 Chromatographic Hydrophobicity Index (CHI)................................ 377 Martí Rosés, Elisabeth Bosch, Clara Ràfols, and Elisabet Fuguet Chapter 9 Recent Developments and Applications in Nonlinear Reversed Phase Liquid Chromatography.......................................... 415 Nicola Marchetti, Luisa Pasti, Francesco Dondi, and Alberto Cavazzini Index....................................................................................................................... 441

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Foreword With this volume, the Advances in Chromatography series reaches the 50th issue milestone. The series was established in 1965 by J.C. Giddings and R.A. Keller with the declared aim of bringing forth current advances in chromatography at the highest scientific level. Since then, several editors have joined and left the series (J. C. Giddings, R. A. Keller, J. Cazes, P. R. Brown, S. M. Lunte). The present editors, N. Grinberg and E. Grushka, have maintained the aim of the series: to provide easy, high quality, and timely access to forefront developments in chromatography and related areas. The scientific quality of each chapter established Advances in Chromatography as a book series not only capable of providing the latest theoretical developments, but also able to demonstrate a large array of applications. For this volume, we tried to bring aboard contributors who, over the years, have brought major advancements to the field of separation science. Advances in Chromatography is the longest running series in the field, producing roughly one volume per year. The series was published by Marcel Dekker, Inc. until 2005, when it was acquired by Taylor and Francis, which is the current publisher of the series through CRC Press. Over the years the series has covered the majority of topics in separation sciences. One can read Advances in Chromatography from the first volume up through the latest, and see a history of separation science. In the earlier days of the series, in the 1960s, the majority of the chapters dealt with gas chromatography. With the advancement in separation sciences (in all of its forms—LC, TLC, FFF, and later of capillary electrophoresis), the topics covered by the series expanded to include these developments as well. Throughout, the editors attempted to maintain a balance between the theoretical, instrumental, and applied aspects of chromatography. The extent of the use of chromatography has progressed greatly since the 1960s, a fact that required the editors to be aware of the developments in a large segment of scientific research. The success of the series is due mostly to the contributors of the reviews. Throughout the life of the series, we the editors (past and present) were extremely fortunate to have excellent authors who did their utmost to ensure the success of the series. Without their efforts the series would not have survived past its first or second volume. We would like to take this opportunity and thank the authors of all 50  volumes for their excellent contributions. We are looking forward to working with our future authors and continuing to provide timely and up-to-date reviews in chromatography and related areas. Nelu Grinberg Eli Grushka June, 2011

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Contributors Pankaj Aggarwal Department of Chemistry and Biochemistry Brigham Young University Provo, Utah Elisabeth Bosch Department of Analytical Chemistry Universitat de Barcelona Barcelona, Spain

Francesco Dondi Department of Chemistry University of Ferrara Ferrara, Italy Elias I. Franses School of Chemical Engineering Purdue University West Lafayette, Indiana

Egisto Boschetti Bio-Rad Laboratories Hercules, California

Elisabet Fuguet Department of Analytical Chemistry Universitat de Barcelona Barcelona, Spain

Peter W. Carr Department of Chemistry University of Minnesota Minneapolis, Minnesota

Nina C. Gonnella Boehringer Ingelheim Pharmaceuticals Inc. Ridgefield, Connecticut

Alberto Cavazzini Department of Chemistry University of Ferrara Ferrara, Italy

Rahul B. Kasat School of Chemical Engineering Purdue University West Lafayette, Indiana

Joe M. Davis Department of Chemistry and Biochemistry Southern Illinois University at Carbondale Carbondale, Illinois

Joseph J. Kirkland Advanced Materials Technology Wilmington, Delaware

Joseph J. DeStefano Advanced Materials Technology Wilmington, Delaware John W. Dolan LC Resources Walnut Creek, California

Milton L. Lee Department of Chemistry and Biochemistry Brigham Young University Provo, Utah Yuanyuan Li Department of Chemistry and Biochemistry Brigham Young University Provo, Utah vii

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Daniel H. Marchand University of Wisconsin—River Falls River Falls, Wisconsin Nicola Marchetti Department of Chemistry University of Ferrara Ferrara, Italy Luisa Pasti Department of Chemistry University of Ferrara Ferrara, Italy Clara Ràfols Department of Analytical Chemistry Universitat de Barcelona Barcelona, Spain Pier Giorgio Righetti Department of Chemistry, Materials and Chemical Engineering “Giulio Natta” Politecnico di Milano Milan, Italy Martí Rosés Department of Analytical Chemistry Universitat de Barcelona Barcelona, Spain

Contributors

Sarah C. Rutan Department of Chemistry Virginia Commonwealth University Richmond, Virginia Lloyd R. Snyder LC Resources Walnut Creek, California Dwight R. Stoll Department of Chemistry Gustavus Adolphus College Saint Peter, Minnesota H. Dennis Tolley Department of Statistics Brigham Young University Provo, Utah Hung-Wei Tsui School of Chemical Engineering Purdue University West Lafayette, Indiana Nien-Hwa Linda Wang School of Chemical Engineering Purdue University West Lafayette, Indiana

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1 Beyond the Frontiers of Mixed Beds

Classical Chromatography for Proteins Egisto Boschetti and Pier Giorgio Righetti Contents 1.1 Introduction....................................................................................................... 1 1.2 Crossing over Single Molecular Interactions: From Mixed-Mode to Mixed-Bed Interaction.................................................................................. 4 1.3 Enhancement of Very Low Abundance Proteins............................................ 10 1.4 Separation of Protein Categories..................................................................... 16 1.4.1 Removal of High-Abundance Proteins................................................ 17 1.4.2 Concomitant Separation of Protein Groups with Similar Types of Molecular Interactions.......................................................... 18 1.5 Mixed Beds as a Source of Selective Ligand Identification for Affinity Chromatography................................................................................20 1.6 Mixed Beds for Isoelectric Group Separation.................................................25 1.7 “Blind” Protein Purification Processes with Mixed Beds............................... 28 1.8 The Place of Mixed-Mode Chromatography within a Protein Separation Scheme............................................................................................................. 31 1.8.1 Polishing Aspect or Removal of Impurity Traces from Purified Biologicals............................................................................. 32 1.8.2 Selection of Media for Mixed Beds..................................................... 35 1.8.3 Streamlining Single-Bed with Mixed-Bed Chromatography.............. 36 1.9 Conclusion....................................................................................................... 37 Acknowledgments..................................................................................................... 38 References................................................................................................................. 38

1.1  Introduction Chromatographic separations for proteins have been essentially operated around interactions between the solid-phase sorbents and protein analytes. Thanks to polypeptide properties, fundamental interactions have been played around ion exchange effects, hydrophobic associations, metal chelation, and dipole–dipole, singularly or sequentially. They are all classified as single-mode sorbents since normally they display only 1 © 2012 Taylor & Francis Group, LLC

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one type of interaction. Elution of proteins is then operated by gradients capable of displacing adsorbed species according to their interaction mode and strength. When specificity is required, bioaffinity solid-phase sorbents have been designed. They are based on protein functions or complex molecular recognition involving the chemical attachment of affinity ligand molecules to the chromatographic solid support, thus allowing the specific capture of the target protein. In all cases, all the particles composing the solid-phase chromatographic support are identical. In a number of instances, the importance of the solid phase support has been underlined. Mechanical and chemical stability, right porosity, density of the active interaction sites, very low level on nonspecific binding, and narrow particle size are among the important characteristics (Boschetti 1994; G. Subramanian 1998; Ahuja 2000; Vijayalakshmi 2002). Over time exploitation of chromatography sorbents for protein separation has not only been perfected, but also their mode of use was progressively optimized for best results. In this context, binding capacity for protein adsorption was largely improved. On the same line, elution gradients were progressively optimized or even superimposed such as pH gradients associated to ionic strength gradients. Displacement processes with the use of special chemical agents have been also developed (Jayaraman et al. 1995). The isolation of one protein from a complex mixture generally involves more than one single column; the latter are chosen according to their complementary adsorption properties. Typically, ion exchangers are followed by hydrophobic sorbents and gel filtration media, each of them acting on one of the main fundamental properties conferred by the amino acid composition and number. In this exemplified case, the first sorbent plays on the net charge of the proteins (ionic amino acids, e.g., Asp, Glu, Lys, and Arg), the second on their hydrophobic index (hydrophobic amino acids, e.g., Phe, Ile, Val, and Leu), and the third on the global mass of the protein (number of amino acids). The key parameters for the development of successful separation conditions are to be selected not only at the adsorption phase but also at the following elution steps of proteins. Adsorption conditions are adjusted according to the interaction mode; for instance, when facing ion exchangers, the net charge of the solid phase sorbent should be of complementary sign compared to the ionized protein. Preferably, the pH should be selected in order to have the maximum number of protein impurities of the same sign as the sorbent so that they would be repelled in the flow-through. Ionic strength is also to be adjusted to displace as much as possible protein impurities. By these two ways, the target protein is captured with the minimum number of other coadsorbed proteins. Elution conditions are also as critical as the capture conditions: Their selection is rationalized to leave impurities still adsorbed while the target protein is desorbed and separately collected. When playing with hydrophobic interaction sorbents, the game is quite similar except that adsorption–elution conditions must be adapted as a function of the hydrophobic media used. Another type of game is played with two main thermodynamic parameters that are the selectivity and the efficiency of separations, both together contributing to the best resolution. They depend not only on the separation conditions but also on the solid phase chromatographic material. For instance, the selectivity level could © 2012 Taylor & Francis Group, LLC

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be great when the capability of the active interacting site is specific for the target protein. Efficiency itself is played mainly on the particle size and the particle size distribution of the chromatographic sorbent. Selecting media as a function of these two properties largely contributes to obtain good resolutions. Naturally, both parameters can be optimized by the operator when all other influencing factors are optimized to the given separation problem (mobile phase composition, temperature, gradient slope and shape, column geometry, flow rate, loading volume, and sample concentration). In spite of numerous parameters in which it is possible to work and improve separations, in a very large number of cases the target protein is much less pure than initially expected. Very good levels of purity can effectively be reached with a price of additional fractionation steps. The number of steps and the complexity of current chromatographic processes to isolate single proteins call for alternative approaches. Among them are mixed-bed chromatography separations, the object of this chapter. It is here interesting to recall that already in 1986 (el Rassi and Horváth 1986) the use of a sequence of anion and cation chromatography resins was turned into a mixed bed with similar results. Thus, acidic and alkaline proteins were separated at the same time using a salt gradient. In the same work, ternary mixtures, including hydrophobic sorbents, were also reported for the fractionation of proteins. The idea of using mixed-bed with tailored elution methods has been suggested for the resolution of difficult separation problems for preparative purposes. Two years later, from the same research laboratory, Maa et al. (1988) refined the approach with increasing salt concentration and comparison to mathematical models for the separation of four proteins. This work confirmed that the selection of mixedbed compositions and the definition of the elution gradients are critical parameters to the fractionation success. Then, several years later, a similar approach was taken by Motoyama et al. (2007) when they attempted to separate phosphopeptides from enzymatically digested proteins for mass spectrometry analysis. The mixed-bed ion exchange column clearly gave better recovery compared to strong cation exchange alone and appeared adapted for a better orthogonality with reverse phase chromatography. More recently (Igawa, 2009), mixed-bed columns involving zwitterionic sorbents and anion exchangers have been reported for the retention of anionic, cationic, and neutral analytes. Under the influence of quite complex interactions, analyte separation was reached by modifying buffer concentrations while controlling hydrophilic interaction by the presence of acetonitrile. Although this complex approach could be successfully applied to relatively small metabolite molecules, its use for protein separation remains to be demonstrated. Perhaps one of the most representative examples of mixed-bed chromatography application appeared with the simultaneous subtraction of several proteins from complex mixtures such as serum using mixed-mode immunoaffinity chromatography. This type of technology was intended to remove high-abundance protein species that generally prevent the detectability of minor component that are present at trace levels (Pieper, Su, et al. 2003). Several antibody-specific affinity sorbents were first prepared and then mixed together before use. Up to 10 affinity antibody © 2012 Taylor & Francis Group, LLC

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sorbents were used together and the proteins captured were eluted en bloc in one single step. Proteins removed from human plasma were albumin, immunoglobulins G and A, transferrin, a-2-macroglobulin, transthyretin, a-1-antitrypsin, hemopexin, haptoglobin, a-2-HS glycoprotein, fibrinogen, and a-1-acid glycoprotein. Since this quite early published work, a large number of papers have reported the use of multiaffinity mixed-bed sorbents for the removal of selected proteins from biological samples. These notions will be developed later in this chapter. On the same line, several families of human plasma glycoproteins were captured with the use of a ternary mixed-mode lectin column obtained by mixing immobilized concanavalin A, wheat germ agglutinin, and jacalin. This peculiar chromatographic column was used for the en bloc separation of glycoproteins from human plasma in view of comparing side-by-side glycoproteomes of normal with pathological samples (Kullolli et al. 2008). The following sections will be devoted to the switch from single-mode to mixedmode chromatography to get finally into mixed-bed separations; main applications with concrete examples will be described.

1.2  Crossing over Single Molecular Interactions: From Mixed-Mode to Mixed-Bed Interaction Chromatographic separation methods utilizing more than one type of interaction between the components of the sample to fractionate and the active sites of the solid phase are called multimode or mixed-mode separations. Mixed-mode sorbents have been designed with the aim of addressing the selectivity aspect for a given protein. Perhaps the earliest mixed ionic-hydrophobic mode was reported in 1972 and 1973 by several laboratories (Yon 1972; Hofstee 1973). Much later, the association of other interaction mechanisms was also included in the mixed mode such as hydrogen bonding (Johansson et al. 2003a, 2003b). It is quite hard classifying mixed-mode ligands for chromatography; however, as described by Zhao, Dong, and Sun (2009), they can be subdivided in two distinct categories related to their main physicochemical structural composition. There are mixed-mode ligands with positive charges from secondary or tertiary amines or even from heterocyclic rings. Close to them are those with negative charges, essentially from the presence of carboxylates or sulfonate groups close to hydrophobic centers. The most described category of mixed-mode ligands associating negative charges is represented by dyes. These quite complex molecules comprise aromatic rings and hydrophobic and hydrophilic centers, as well as ionizable groups. They have been extensively described since the 1970s to enlarge the scope of affinity chromatography media (Easterday and Easterday 1974; Subramanian 1982; Stellwagen 1990; Denizli and Piskin 2001). With their composite structure, they induce the formation interactions at more than one point with at least ionic exchanges, hydrophobic associations, and hydrogen bonding. Dye ligands for chromatography—extensively reviewed, for instance, by Stellwagen (1990)—compose the basis of experimental separation data reported in thousands of published papers. Several categories of dyes are used in affinity © 2012 Taylor & Francis Group, LLC

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Mixed Beds

chromatography; the best known are azoic dyes (Burke and Crawford 1998) and anthraquinone dyes (Bohácová et al. 1998; Labrou 2002). Thanks to their quite complex structure, they have the property to capture single proteins such as human serum proteins like albumin (Angal and Dean 1977; Travis and Pannell 1973; Birkenmeier et al. 1983), transthretin (Regnault et al. 1992), and IgG (Byfield, Copping, and Himsworth 1984). Studies on groups of enzymes such as dehydrogenases (see, for example, Stockton et al. 1978; Glemza 1990) and kinases (e.g., Johanson, Hansen, and Williamson 1988) have also been performed. From the structure of dyes, similar other customized structures have been rationally designed to target a given protein selectively in a better fashion. Thus, IgG antibodies (Li et al. 1998; Teng et al. 2000), elastases (Filippusson, Erlendsson, and Lowe 2000), and glycoproteins (Gupta and Lowe 2004) have been purified from crude extracts using redesigned ligand molecules. A number of other types of mixed-mode sorbents are those that have been designed for the separation/purification of antibodies (see Table 1.1). Among them are heterocyclic molecules (Oscarsson and Porath 1990; Schwarz, Kohen, and Wilchek 1995a, 1995b), thiophilic structures (Boschetti 2001), peptides (Yang, Gurgel, and Carbonell 2005), and oligonucleotides, which are also known under the name of aptamers (Miyakawa et al. 2008), just to mention a few. The peculiar aspect of mixed-mode sorbents is to carry ligands possessing at least hydrophobic and ionic interaction sites. With these chemical residues on the same ligand, the interaction with a given protein is induced by two or more distinct phenomena. Since hydrophobic associations and ionic interactions can only be dissociated by antagonistic displacers, the Table 1.1 Small Mixed-Mode Ligands Used for Separation of Antibodies Type of Ligand Yellow GGL 2- or 4-Thiopyridine 3-Aminophenylboronic acid Mercaptoethyl-3,5-dichloro-2,4,6-trifluoropyridine Drimarene rubine R/K5-BL Chelated nickel ions Mercaptoethyl-ethyl sulfone 2-Mercaptothiazoline Phenylalanine, tyrosine triazinyl derivatives 3-(2-Mercaptoethyl)quinazoline-2,4(1H,3H)dione Mercaptopyrimidine; 2-mercapto-nicotinic acid Mercapto-benzimidazole sulfonic acid Mercaptoethyl-pyridine Linear hexapeptide (HWRGWV) Oligonucleotide Branched peptide

Ref. Byfield, Copping, and Bartlett 1982 Porath and Oscarsson 1988; Oscarsson and Porath 1990 Brena and Batista-Viera 1992 Ngo 1993 Cochet et al. 1994 Hale and Beidler 1994 Schwarz et al. 1995a Schwarz et al. 1995b Li et al. 1998 Scholz, Vieweg, et al. 1998a Scholz, Wippich, et al 1998b Girot et al. 2004 Boschetti 2002 Yang et al. 2005 Miyakawa et al. 2008 D’Agostino et al. 2008; Moiani et al. 2009

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elution of proteins becomes relatively complex. In other words, a protein captured by a solid phase by means of ionic and hydrophobic interactions may be difficult to elute because, while using salts to weaken the ionic interaction, the hydrophobic association may be reinforced. Opposite situations have been described when an attempt has been made to weaken the hydrophobic association. It is exactly in this context that more sophisticated interaction modes have been designed. One of them is the so-called “hydrophobic charge induction chromatography.” The ligand is here structured in a way so that, during protein adsorption, hydrophobic forces are the main interaction between the solid phase and proteins, while the dissociation is induced by the creation of a repulsing charge effect just by modifying the environmental pH. This phenomenon has been extensively described for several dual-mode ligands, the most important of which is mercaptoethyl-pyridine. In this specific example, the interaction is likely more complicated due to the presence of a heterocycle and the presence of a sulfur atom in the structure of the ligand, resulting in a more complex interaction than just a hydrophobic association. Nevertheless, the dissociation of captured species is operated by the repulsion force of similar ionic charges induced by a pH switch of the elution buffer. Under physiological conditions of ionic strength and pH, antibodies interact with immobilized mercaptoethyl-pyridine in quite a specific manner and at a relatively high binding capacity of 10–30 mg per milliliter of resin (Bosch etti, 2002). The ligand has a pKb close to 4.8; when the pH of the environment is below 5, the antibody association strength decreases, and when the pH is decreased below 4.5, the antibody dissociates and is thus collected. Typically, elution is achieved at a pH close to 4, which induces an electric charge strong enough to repulse the antibody from the sorbent. The separation performance is here played on two different aspects: (1) during the capture of the protein (mixed-mode mechanism), and (2) during the pH change. In fact, other coadsorbed proteins with relatively low pI (isoelectric point) are not charged enough to coelute with IgG (Guerrier, Flayeux, and Boschetti 2001). To elucidate the interaction area, experiments have been performed using antibody fragments; the reported results demonstrated that only Fc fragments were captured by the sorbent, but not Fab, under the same conditions (Guerrier et al. 2001). In another set of experiments made using analogs of mercaptoethyl-pyridine, the cooperative roles of the pyridine ring of the sulfur atom and the hydrophobic spacer were determined. When the spacer was hydrophilic including the presence of an OH group, the binding capacity decreased significantly, underlining the importance of the hydrophobic moiety in the ligand to adsorb IgG in physiological conditions of ionic strength. When the hydrophobicity of the spacer was not modified, but the sulfur atom was replaced by a nitrogen or an oxygen atom, binding capacity for IgG decreased close to zero under the same environmental conditions. Furthermore, the capability to capture IgG even in the presence of massive amounts of ammonium sulfate was not restored. Conversely, when 4-mercapto-ethyl-pyridine was immobilized after divinyl-sulfone activation, with a subsequent addition of a sulfur atom, the binding capacity for IgG under similar physicochemical conditions was clearly enhanced (Boschetti and Guerrier 2002). Another similar concept of mixed-mode ligand for antibody capture was developed by using 2-mercapto-5-benzimidazolesulfonic acid, an aromatic heterocyclic © 2012 Taylor & Francis Group, LLC

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molecule carrying a strong anionic group (Brenac et al. 2005). By using crude extracts, in a single step the antibody purity reached 85%–95%. This immobilized ligand could be easily used for the production of pure antibodies for diagnostic and therapeutic applications in conditions compatible with large-scale requirements. Albumin, a difficult protein to remove, was largely decreased or even eliminated as a result of the presence of a sulfonic acid group within the structure of the ligand. With this concept in mind and by playing on the dual or multiple character of the ligand, it was possible to achieve ion exchange and hydrophobic chromatography under physiological conditions of adsorption. In other words, with the use of ligands where the ion charge or the hydrophobic charge dominated and secondary interaction points (adsorption “helpers”) were present, it was possible to operate ion exchange chromatography in the presence of quite high ionic strength and hydrophobic chromatography at quite low ionic strength. In the latter case, the use of hydrophobic ligands with hydrocarbon alkyl chains or with aromatic rings associated with a short ionic linker allowed interesting hydrophobic interactions under physiological conditions for the unconventional separation of proteins (Brenac et al. 2005; Brenac-Brochier et al. 2008). Bovine β-lactoglobulin was thus purified from milk whey by hydrophobic association under physiological conditions and elution operated by decreasing the pH, which modified the ionic environment and allowed protein desorption. By steps of decreasing pH, it was also possible to separate b-lactoglobulin from a-lactalbumin, the latter being more hydrophobic. IgG antibodies’ interaction with these mixed-mode ligands was also investigated with respect to the molecular mechanism and the dependence on temperature (Ranjini et al. 2010). The use of heterocyclic compounds is also another aspect of mixed-mode chromatography described first by Porath and co-workers (Oscarsson and Porath 1990; Porath and Oscarsson 1998). It was demonstrated that aromatic or heterocyclic compounds, attached to a solid support by means of a thioether bond, were able to adsorb some selected proteins from human blood. Here the presence of the sulfur atom, the aromatic ring, or heterocyclic groups cooperates in the mechanism of protein adsorption. Oscarsson and Porath (1990) also investigated a number of sorbents based on pyridine and alkyl-thioether agarose with the aim of identifying the greatest specificity for the adsorption of immunoglobulins. Other heteroaromatic ligands attached on chromatographic supports via divinylsulfone have been described by Knudsen et al. (1992), such as 2-hydroxypyridine, 4-hydroxypyridine, 2-aminopyridine, and imidazole. All have been evaluated for their ability to isolate antibodies from human serum. Finally, other heterocyclic compounds have been described as mixed-mode ligands for the adsorption of protein, especially antibodies 3-(2-mercaptoethyl)quinazoline2,4(1H,3H)dione, mercaptopyrimidine, and 2-mercapto-nicotinic acid (Scholz, Vieweg, et al. 1998a; Scholz, Wippich, et al. 1998b). Among very many different mixed-mode ligands for chromatography, an interesting category comes from the use of peptides. Since amino acids individually can carry ionic, hydrophobic, or aromatic heterocyclic structures, they are an ideal ground for the production of mixed-mode ligands whose complexity depends on the types and numbers of amino acids used. Various amino acids have been used as © 2012 Taylor & Francis Group, LLC

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Egisto Boschetti and Pier Giorgio Righetti NH2 C

NH

NH

NH

CH2

N

CH2

CH

H N

CH N H

C O

CH2

H N

CH N H

C O

O C CH CH2

C HN

NH2

HC H N

CH N H

C O

O C CH HC

CH2

CH2

CH2

O C CH

CH2

CH2

CH2

CH2

CH2 O C

H N

CH3

N H CH3

CH3 H N

CH C O

CH CH2

CH2 O

CH3

OH OH

Figure 1.1  Schematic view of a nonapeptide with different amino acid side chains displaying various physicochemical properties. From the left: lysine with a terminal primary amine group; histidine with a heterocycle; tryptophan with aromatic heterocyclic group; arginine with a terminal guanidine group; glutamic acid with a terminal carboxyl; phenylalanine with an aromatic ring; isoelucine with a strong hydrophobic chain; valine with a mild hydrophobic chain; tyrosine with a hydroxylated aromatic ring.

ligands for chromatography. They may act according to two different principles: (1) as specific ligands for given proteins, or (2) as mixed-mode ligands when they carry complex structures such as arginine with the guanidinium group or tryptophan with the heterocycle connected to an aromatic ring. Small peptides resulting from the condensation of a few amino acids possess more centers of mixed-mode interactions due to side chains of selected building blocks. As represented in Figure 1.1, side groups of amino acids participate with the final overall peptide ligand property. Interaction between partners composed of amino acids mimics somewhat biology situations where individual proteins interact more or less intensively with each other to accomplish their function. Immunoaffinity chromatography with immobilized antibodies (a very large mixed-mode complexity) represents the most specific way to recognize a given protein antigen (see Section 1.4.1). If one could make all possible peptides, starting from the natural amino acids, the problem of having any possible ligand available for chromatography would be resolved. To this end, chemistry made possible the synthesis of peptides under a combinatorial manner to reach the goal of very large ligand diversity. Instead of making separate syntheses of peptides, the dilemma was resolved by developing the so-called strategy of spit-and-pool combination (Furka et al. 1991; Lam et al. 1991). This strategy resulted in the preparation of very many mixed-mode ligands already attached on a solid chromatographic support and also mixed beds of mixed-mode ligands (see Section 1.5). Peptides generally used for this purpose are relatively short, with three to six amino acids. Nevertheless, the number of ligands produced became very large when 20 building blocks were used with respectively 8,000 and 64,000,000 diversomers. © 2012 Taylor & Francis Group, LLC

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Mixed Beds (a)

(b) (e) Mixing beads together (c)

(d)

Figure 1.2  Mixed bed (e) resulting from the association of single-feature individual sorbents (a, b, c, and d) that are mixed together under identical or different proportions.

Mixed beds are composed of chromatographic sorbents of various natures and possibly with complementary properties that are mixed together (see Figure 1.2). The use of mixed-beds requires that all immobilized ligands on distinct beads work under similar physicochemical conditions for protein adsorption. However, they do not necessarily have to be composed of mixed-mode ligands, but rather could comprise simple single-mode ligands. From this principle, mixed-bed chromatography could be classified under two main groups: (1) mixed bed of single-mode sorbents, and (2) mixed bed of mixed-mode sorbents (see Figure  1.3). As will be described later, a mixed bed could be used for two distinct methodologies: (1) loaded with a protein amount that does not exceed the binding capacity of the solid phases, or (2) largely overloaded for applications in proteomics investigations. Mixed-beds of single-mode sorbents. The easiest way to make simple mixed beds is to blend together and pack single-mode chromatographic sorbents such as various ion exchangers or ion exchangers with hydrophobic sorbents or with other single-mode sorbents. In addition to the examples reported in the introduction, it is also possible to blend hydrophobic sorbents of different hydrophobic chain length or different immobilized sugars or chelating solid supports carrying different metal ions. By modulating the separation conditions and especially by selecting the proper displacers, it is possible to elute and collect different protein categories. Nevertheless, most of these applications have been operated with column cascades © 2012 Taylor & Francis Group, LLC

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Egisto Boschetti and Pier Giorgio Righetti Increasing degree of complexity

Single-mode

Mixed-mode

Mixed-beds of single-mode

Mixed-beds of single & mixed-mode

Mixed-beds of mixed-mode

Figure 1.3  Obtention of mixed beds of different complexities resulting from the blend of single-mode sorbents or from mixed-mode sorbents or even from both single- and mixedmode sorbents.

where the most selective sorbent is placed first and the least selective one is placed last in the column sequence. Mixed beds of mixed-mode sorbents. In a higher degree of complexity, mixed beds could be obtained by blending mixed-mode sorbents. This is the case with combinatorial ligand libraries and also with beds resulting from rational mixtures such as those described in Section 1.7. These configurations are useful for ligand discovery for affinity purposes and to resolve complex problems of polishing processes.

1.3  Enhancement of Very Low Abundance Proteins Proteome analysis of biological extracts, especially from blood, represents a real challenge not only because of the large number of polypeptides present, but more importantly due to the extremely large dynamic concentration range of protein components that span over 10 orders of magnitude (Pieper, Gatlin, et al. 2003). To try reducing this difference several approaches have been proposed, one of which is the use of mixed-bed peptide libraries (Thulasiraman et al. 2005; Righetti et al. 2006; Righetti and Boschetti 2009; Righetti et al. 2010d). Beads constituting the mixed bed are different from the each other, since each bead carries a different ligand. In other words, each bead corresponds to a very small single bed where the total binding capacity is, by definition, very limited. The use of such mixed beds in overloading conditions has been extensively described in proteomics investigations to enhance low- and very low-abundance species. Applications of these libraries in proteomic investigations deal essentially with the detection of species whose concentration is below the sensitivity of current analytical methods. The working principle is based on the intrinsic binding capacity limitation of chromatography sorbents: When the saturation is reached, the excess of the protein cannot bind and is consequently discarded in the flow-through. In the case of a mixed-bed ligand library, this mechanism is extended to each bead and therefore throughout a very large number of different affinity ligands. When such mixed-bed packing is put in contact with a complex protein mixture, each unique © 2012 Taylor & Francis Group, LLC

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Mixed Beds

Biological sample (large dynamic range)

Recover bound protein

Ligand library

Wash away unbound protein Overloaded species Large excess protein extract

+

Bead ligand library

Single fraction

Elution

a Multiple fractions b c

Figure 1.4  (See color insert.) Rough representation of the reduction of the dynamic concentration range of proteins constituting a mixture by means of a solid-phase combinatorial ligand library. A relatively large excess of biological sample, comprising proteins at very different concentrations, is put in contact with the ligand library. The excess of proteins (namely, the most abundant ones) are washed out and captured proteins are desorbed from the beads and collected. The collected sample contains the same proteins as initially, but the proportions are very different, thus allowing many more proteins to be detected.

affinity ligand bead within the pool will bind and concentrate its specific protein partner up to the point of bead saturation and independently on all other affinity ligands and proteins. When the relative concentration from each species within the protein mixture forms a large dynamic range, the high-abundance proteins rapidly saturate their corresponding beads while low-abundance ones continue to adsorb as long as the sample is available and loaded. After removal of all proteins that are not bound, the composition of proteins retained by the beads is defined by the presence of their specific affinity ligands and the relative concentration of each retained protein species. Considering the library as having a representative ligand for each protein of the biological extract, the eluted protein mixture would have the same composition as the initial sample, but the relative protein concentration range would be largely compressed (Figure 1.4). This quite satisfactory but simplistic explanation about how a solid-phase combinatorial peptide ligand library works for the decrease of the dynamic concentration of protein components is based on the absolute specificity of a peptide bead for a single protein associated with a binding capacity saturation phenomenon. Nevertheless, the mechanism is probably far more complex. Even if some peptides © 2012 Taylor & Francis Group, LLC

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of the library could be extremely specific for given proteins, many others interact with various proteins. Indeed, a single bead in a number of cases captures more than one protein, as has been clearly demonstrated (Boschetti et al. 2007) by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and mass spectrometry analysis of a single bead from the library. Patterns are different, however, from bead to bead and some proteins are common, suggesting that a single protein might be captured by various peptide ligands. The mass action law indicates that interactions between partners are the result of equilibrium of forces governed by association and dissociation constants. With complex mixtures of ligands and proteins, a very large number of situations are present with affinity constants that might range between extreme values (low and high). As a result of observations and theoretical considerations, it becomes believable that the mechanism of reduction of protein concentration range is more complex than anticipated and depends on the number of ligands, the affinity constants, and the concentration of each individual protein of the mixture. Secondary parameters that influence the thermodynamic equilibrium and hence the affinity between partners are environmental conditions such as temperature, pH, ionic strength, presence of special molecules in solution, diffusion time, etc.—all of which influence dynamic phenomena of displacement. Kinetics may also play an important role, particularly when the protein size is large and the affinity for a peptide is weak. The overall result of the complex mechanism here described is a reduction of the dynamic concentration range of captured proteins when compared to their initial situation in solution. High-abundance proteins are reduced in their concentration while low-abundance ones are largely concentrated; the extent of the phenomenon depends on the amount of protein extract offered to the mixed-bed ligand library beads. After the treatment, very-low abundance species are easily detectable (Roux-Dalvai et al. 2008), opening the way to many proteomics applications, such as, for instance, the discovery of new species (see Figure 1.5), the detection of biomarkers of diagnostic importance, and the discovery of new allergens. Only under large overloading conditions is it possible to capture and accumulate on corresponding beads low-abundance proteins up to the saturation. At the same time, the overloading conditions are without any effect on high-abundance proteins that have already saturated their corresponding beads, the excess remaining in solution. The counterpart of this peculiar phenomenon is that the volume of the biological sample must be large compared to the volume of beads. Most generally, it is suggested that the amount of protein loaded on a given volume of beads corresponds to at least 50 times the binding capacity of the bead bed. If the amount of protein loaded is lower than the binding capacity of the beads, the resulting treated sample will have an unchanged composition (Thulasiraman et al. 2005). Proteins captured by their corresponding peptide ligand are differently adsorbed and are eluted under conditions that are not necessarily the same. Some of them are dissociated from the beads in the presence of sodium chloride, while others require a change in pH to release the captured protein or even the use of concentrated chaotropes in acidic and alkaline conditions. © 2012 Taylor & Francis Group, LLC

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Mixed Beds

Red blood cell lysate

Human serum

A

Human urine

Egg white

Hevea brasiliensis latex

Native extracts

After peptide library treatment

Figure 1.5  Two-dimensional analysis of biological samples before and after treatment with a combinatorial ligand library (here, a peptide library—ProteoMiner). The number of spots is considerably increased as a witness of increasing concentration of low-abundance species that were undetectable in the untreated sample.

According to these data, interaction models have been proposed (Righetti et al. 2010d). A simple model suggests that the protein docks on its immobilized partner ligand only; however, this is not always consistent with the tenacious binding of proteins to the peptide beads, which requires very strong eluting conditions. Thus, another model was suggested with several peptide ligands binding to different regions of each protein, thus inducing a cooperative effect with stronger apparent affinity. Since each bead carries only a single type of peptide, multiple interactions are possible if one assumes that not all amino acids of the peptide ligand are needed for proper binding. Experimental evidence has already indicated that, with a tripeptide, the number of different captured proteins tends to plateau (Simó et al. 2008). This suggests that not all amino acids are involved in the interaction; there could well be situations where portions of the peptide ligand interact with other regions of the same partner protein, thus producing cooperation. © 2012 Taylor & Francis Group, LLC

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Actually, amino acids alone can act as affinity ligands for protein adsorption (Bachi et al. 2008). Nevertheless, these models do not describe the dynamics of the interaction phenomenon that comprises an intense competition among proteins from the biological sample and the peptides of a single bead as experimentally deducted elsewhere (Simó et al. 2008). This competition seems to favor the capture of lowabundance proteins, maybe because of their propensity to display stronger interaction properties compared to highly concentrated species. Competition and large overloading conditions play together to the final result. When the collection of peptides is covalently attached on a single bead (all-peptides– one-bead), the final protein pattern is much different; therefore, the displacement phenomenon could be differently interpreted. Many more proteins participate in local displacement effects while interacting with more than one ligand or a portion of it within the same bead, and the saturation phenomenon may not be the same as it is in the case of the one-peptide–one-bead configuration. The final composition of eluted proteins from such a solid-phase peptide library is largely different from what results from the one-peptide–one-bead library (Boschetti and Righetti 2008). It does not seem to give the same advantage to low-abundance species; on the contrary, it reveals less numerous spots in two-dimensional electrophoresis and creates new high-abundance proteins. Finally, to extract the real sense of the complexity of the protein capturing process in overloading conditions by mixed-bed peptide libraries, it is understood that the length of the peptide plays another non-negligible effect. Although a tripeptide library is enough to produce strong effects on the reduction of the protein dynamic concentration range, the elongation of the peptide chain participates to a better docking with protein epitopes and reveals additional low-abundance species. Nevertheless, this approach has its limits because the peptides tend to modify their shape upon elongation with individual folding. All of the explanations or interpretations described previously do not consider interactions between proteins that very probably occur in physiological conditions. Beyond the protein capture aspect of mixed-bed ligand libraries, a further point to consider is the elution of proteins. Although in most cases in proteomics applications, the elution is a true stripping with very strong desorption agents to remove all proteins at once (Candiano et al. 2009; Farinazzo, Fasoli, et al. 2009), the intrinsic mixedmode characteristics of each single bead composing the mixed bed allows eluting proteins by their similar properties. Proteins captured by a dominant hydrophobic association can be desorbed by hydrophobic competitors such as propylene glycol while proteins adsorbed mainly by ion exchange are removed by the addition of salts. Other interactions such as hydrogen bonding are annihilated by the use of urea or guanidine. In this respect, categories of proteins can be generated with quite similar properties (Guerrier, Claverol, et al. 2007). pH changes can also be used to modify the net charge of a protein at both adsorption (Fasoli et al. 2010) and elution stages. Several other elution methods have been suggested: some in direct connection with the subsequent analysis (Righetti et al. 2010b) and others with the aim of fractionating the protein mixture (Righetti et al. 2006; Righetti and Boschetti 2007). Recall that the use of mixed-bed libraries based on hexapeptides allowed discovering a very large number of proteins from red blood cell lysate, as reported © 2012 Taylor & Francis Group, LLC

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in Roux-Dalvai et al. (2008). The treatment of a soluble lysate of purified human red blood cells with a mixed-mode hexapeptide library surprisingly allowed identifying up to 1,578 gene products at the time when only 250 species were known (Pasini et al. 2006). Eight different globin chains could be detected: the first two were well-known components of adult hemoglobin; two others, γ- and ε-globins known as fetal chains, whose genes were believed to be silenced a few months after birth, were also detected. Interestingly, another four globin chains (ζ, θ, δ, and μ, called embryonic chains) were also found, while their corresponding genes were thought to be silenced already in the switch from embryo to a developed fetus. While delving into the very long list of gene products found in red blood cell lysate, geneticists found proteins related to some pathological situations. Among them is CDA II, which is related to a rare hereditary disorder characterized by ineffective erythropoiesis and distinct morphological abnormalities of erythroblasts in the bone marrow (Bianchi et al. 2009), thus making a possible link between proteomics investigations and genomics. In the case of human cerebrospinal fluid treated with mixed-bed peptide libraries, 745 additional gene products could be identified to known species (Mouton-Barbosa et al. 2010). In spite of the high abundance of blood-derived proteins, it has been possible to find many low-abundance neuronal species that are normally undetectable. Some new proteins detected were related to different compartments inside the brain and to crucial metabolic pathways, sometimes up-regulated in particular diseases. Among them, proteins involved in neurogenesis were found. This is the case of Semaphorin 3B and neuropilin–1 and 2, which play a role in axonal guidance and cell migration and are interesting in brain pathologies such as glyomas (Yazdani and Terman 2006; Geretti and Klagsbrun 2007). Other, more classical brain markers were found, like neuron-specific enolase and the astrocytic protein S100B, which are released in the CSF following neuronal cell degradation (C. Pennington et al. 2009). Parkinson disease-associated proteins (da Costa 2007), as well as different subunits of the proteasome, open an attractive perspective in the context of neurodegenerative diseases (Ross and Pickart 2004). A table of brain-derived polypeptides found in CSF upon bead library treatment has been recently published (Mouton-Barbosa et al. 2010). In another completely different example—full analysis of a snake venom after treatment with a mixed-bed library of hexapeptides—interesting discoveries were made (Calvete et al. 2009). Outside known proteins present at low concentration, such as those belonging to metalloproteinases and many others, there were also three minor protein families related to cytotoxic, mytotoxic, hemotoxic, and hemorrhagic effects—all of them representing the overall toxic profile of the venom. Interestingly, 2-cys peroxiredoxin and glutaminyl cyclase, never previously detected in snake venoms, were evidenced. They may participate, respectively, in the structural/functional diversification of toxins and in the N-terminal pyrrolidone carboxylic acid formation required in the maturation of bioactive peptides such as bradykinin-potentiating peptides and endogenous inhibitors of metalloproteases. In a recent investigation dealing with discovering traces of casein as a fining agent in white wines, Cereda et al. (2010) demonstrated that upon ProteoMiner treatment, it was © 2012 Taylor & Francis Group, LLC

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Egisto Boschetti and Pier Giorgio Righetti PM-treated serum (eluates) Native serum

pH4

pH7

pH9.3

Mixture of eluates

Figure 1.6  (See color insert.) Capture of sera with three different ProteoMiner (PM) treatments at pH 4.0, 7.0, and 9.3 compared with untreated sample (native serum). The last track to the right represents a 1:1:1 mixture of the eluates from the three different pH captures. The very strong reduction of the albumin band (arrow in the control) can be easily appreciated (SDS-PAGE in a discontinuous Laemmli buffer, in an 8%–18% porosity gradient; silver staining). (From Di Girolamo, F. et al., unpublished.)

possible to capture about 80% of such traces efficiently, even when using tiny amounts of beads (barely 100 μL) in large volumes of liquid (1 L). The signal amplification exceeded 5,000-fold, something that no technique had achieved up to now. Figure  1.6 should dispel any doubt: Even in a monodimensional SDS-PAGE, it can be appreciated that sera captured with a peptide ligand library at three different pH values (4.0, 7.0, and 9.3—routinely recommended today, as extensively described by Fasoli et al., 2010, and Righetti et al., 2010b) exhibit an incredible number of extra bands, whereas the thick and heavy albumin band in the control is reduced to vanishing amounts. In numerous other examples, the use of such libraries allowed discovering novel species such as in egg white (D’Ambrosio et al. 2008) and yolk (Farinazzo, Restuccia, et al. 2009), human urine (Castagna et al. 2005), Limulus polyphemus hemolymph (D’Amato, Cereda, et al. 2010), plant extracts (Boschetti et al. 2009), and novel allergens—for instance, from milk (D’Amato et al. 2009) and from latex (D’Amato, Bachi, et al. 2010).

1.4  Separation of Protein Categories In protein separation technologies, there are situations where it is important or even crucial to remove and/or identify certain categories of proteins from complex mixtures. There are numerous concepts covering these two distinct aspects that are out © 2012 Taylor & Francis Group, LLC

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of focus in this document because they may use homogeneous beds filled with sorbents of large spectra. However, we describe here two peculiar aspects of mixed beds to contribute to resolving some situations.

1.4.1  Removal of High-Abundance Proteins In proteomics, the goal is to decipher the component of selected protein extracts such as, for instance blood serum, urine, cerebrospinal fluid, cell extracts, etc. When applying current analytical methods such as two-dimensional electrophoresis or mass spectrometry, very rapidly a technical issue arises. This is the presence of massive amounts of some proteins compared to others. For instance, in red blood cell aqueous lysates, the amount of hemoglobin represents up to 98% of the total protein amount. Similarly, in human serum, albumin represents about 60% as well as ribulose-1,5-biphosphate carboxylase/oxygenase in leaf extracts. The massive amount of single proteins prevents the detection of many rare species, just as it is impossible to see stars during the day where the major star, the sun, largely dominates with a lot of light with the consequence of starlight signal subtraction. Among technical solutions to resolve the issue is the use of high-abundance protein removal by various means. Albumin and few other very high-abundance proteins that dominate plasma proteome, which are concurrently the source of troubles in two-dimensional electrophoresis and mass spectrometry where they induce signal suppression of a number of other species, are concomitantly removed prior to analysis. The removal process, called “depletion,” is performed by chromatography using mixed-bed specific sorbents. Some are based on a mixture of immobilized Cibacron blue and protein A; others use synthetic ligands (see, for review, Righetti et al. 2006). However, the most powerful means is the use of immunosorbents against major proteins; thus, solid phases comprising various antibodies are used as mixed beds. They are immunosorbents mixed together to target more than one protein; there exist mixed beds against 6, 14, 20, or even 87 major- to mediumabundance human serum proteins. A whole serum loaded to such packed mixed-bed columns is depleted of corresponding proteins and the flow-through containing all other proteins is then analyzed. The process generally allows detecting proteins that are normally not detectable before such a treatment. Already, in 2003, Govorukhina et al. (2003) had tested different approaches for reducing the level of abundant proteins by specific antibodies, dye ligands, or other natural proteinaceous ligands such as proteins A and G. In 2005, other authors performed comparative studies using different depletion technologies and concluded that multiple immunoaffinity sorbents offered the most promising depletion approach (Zolotarjova et al. 2005; Bjorhall, Miliotis, and Davidsson 2005). Thus, different authors reported one of the first chromatographic methods that allowed observing undetectable species upon depletion and describing specific aspects of immunodepletion (Shores and Knapp 2007; Vasudev et al. 2008; Cellar et al. 2009). In spite of better visibility of hidden proteins, other authors reported drawbacks that might limit the use of depletion methods, depending on the objectives. Granger

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et al. (2005) as well as Shen et al. (2005) reported large codepletion of lowabundance proteins when using immunosorbents. Limitations in this technical approach (L. Huang and Fang 2008) are outside the scope of the preset review and will not be discussed here. Nonetheless, as recently reported (Tu et al. 2010), it appears that generalized proteomic analyses after immunodepletion using current platforms cannot be expected to discover low-abundance, disease-specific biomarkers in plasma efficiently. This report concluded in fact that, from analyses of immunodepleted plasma by isoelectric focusing, followed by liquid chromatography-tandem mass spectrometry (LC-MS/MS), the increase in identified proteins compared to nontreated plasma was only about 25%.

1.4.2  Concomitant Separation of Protein Groups with Similar Types of Molecular Interactions Mixed beds have also been conceived for the simultaneous capture of protein categories like mixed immunosorbents discussed in Section 1.4.1, where the common feature is the antigen–antibody interaction. With this example, elution of captured proteins is operated simultaneously since no specific displacement effect can be adopted. In a number of other cases of group separation, protein adsorption is performed concomitantly, whereas elution could be obtained sequentially by the use of specific displacers (see Figure 1.7). One example is the fractionation of glycoproteins. This category of proteins carries glycans that are differently structured and interact quite specifically with other proteins called lectins. The interaction of glycoproteins with mixed beds of immobilized lectins is operated in physiological conditions of pH and of ionic strength Initial sample a

b

c

d

a

b

c

d

Figure 1.7  (See color insert.) Schematic representation of a mixed bed with four single chromatographic media associated to a sequential elution using four specific displacements agents (“a,” “b,” “c,” and “d”). The system works as four distinct columns but the adsorption phase is, by definition, the same for all groups of proteins. © 2012 Taylor & Francis Group, LLC

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so that the fundamental conditions of mixed-bed technologies are met. The elution of glycoproteins is obtained by specific displacement with competing sugars. This principle could be extended to a large number of lectins and complex mixed-bed packings thus obtained. Upon injection of biological fluids or cell extracts only glycoproteins would be adsorbed on their corresponding specific lectin. The elution by category is accomplished by introducing in the column solutions of different competing sugars. This strategy has been described as M-LAC by Dayarathna, Hancock, and Hincapie (2008) to improve conditions for analysis of specified diseases. Lectin of mixed beds comprising concanavalin A, wheat germ agglutinin, and jacalin were mixed together and a single column packed. After protein loading, the elution was performed using competitive sugars. Authors described this technology as an important improvement over the current methods to detect very significant changes in proteome profiles. The initial sample treatment was performed using two mixed-bed columns: The first was an immunodepletion column with a blend of six different bead antibodies against most abundant proteins from human serum and then the depleted flow-through was injected into a second column bed constituted of mixed lectin sorbents. This platform was subsequently used for the analysis of glycoproteomes with high recovery and good reproducibility (Kullolli et al. 2010). The use of spectral counting could produce semiquantitative data crucial for the evaluation of abundance differences among clinical samples. Another example of group protein separation is constituted by proteins sharing similar post-translational modifications, such as phosphoproteins. Phosphorylation of proteins takes place mostly on serine, threonine, and tyrosine residues under very different signaling circumstances. The separation of phosphoproteins as a whole is of high interest in biology since it is the basis of the signaling transduction and protein synthesis; however, in spite of large efforts, it is still a partially resolved problem since current technologies may not capture the entire phosphoproteome. Antibodies against phosphoproteins have been prepared and they are specific for the phosphate group when attached to given amino acids. Consequently, when the capture of the entire phosphoproteome is envisioned, a mixed bed of immobilized antibodies may elegantly resolve some situations and similarly for the capture of high-abundance proteins (Section 1.4.1) (Grønborg et al. 2002; Peirce et al. 2005). The elution of phosphoproteins or phosphopeptides could be performed using a change in environmental pH or by specific displacements. A simple ion-exchange mixed bed, combining opposite charge resins, demonstrated much better performance in separating phosphopeptides resulting from a trypsin digest of a yeast cell lysate when compared to classical cation exchange SCX (Motoyama et al. 2007). A possible explanation was the induction of higher fluxes of cations and a reduced flux of anions coming from an enhanced Donnan effect. This mode of phosphopeptide enrichment is operated in acidic buffer systems that are directly compatible with electrospray ionization for LC-MS/MS direct sequencing analysis. Metal chelate chromatography could also constitute a way to capture en mass interacting proteins with different metal ions. In this context, chelating media could first be loaded separately with different metal ions and then mixed together and packed in a single column to produce a mixed bed of chelated metal ions. Captured © 2012 Taylor & Francis Group, LLC

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Ga+++ Fe+++

Co++

Zn++

Ni++

Cu++ 3000

4000

5000 m/z

6000

7000

Figure 1.8  Mass spectrometry analysis of peptide fraction from a cascade of chelating chromatography columns, each of which is loaded with a different metal ion. Affinity of peptides is not the same for metal ions, especially between the first four shown (Ga+++, Fe+++, Co++, Zn++), whereas some overlapping signals appear between nickel and copper chelated ions. m/z = mass over charge.

proteins under overloading conditions to equilibrate the exchanges could then be desorbed sequentially by using competitive metal ion solutions from the weakest to the strongest. This approach demonstrated its efficacy when used as column cascade (see Figure 1.8) and would easily be turned into a mixed-bed chromatography.

1.5  M  ixed Beds as a Source of Selective Ligand Identification for Affinity Chromatography Specific ligands for the binding of proteins are of high interest in protein purification processes. They constitute the basis of affinity chromatography. Many possible molecules have been described for this purpose, including antibodies (Moser and Hage 2010), synthetic structures (Linhult, Gülich, and Hober 2005; Roque, Gupta, and Lowe 2005), aptamers (Q. Zhao and Chris 2009; Mairal et al. 2008), and peptides (Pande, Szewczyk, and Grover 2010; Tozzi and Giraudi 2006). In order to cover the largest possibilities of molecular structure and thus interactions, combinatorial libraries have been conceived (Lam et al. 1991; Sebestyen et al. 1995). These libraries are synthesized directly in the solid phase so that the resulting products are libraries of bead ligands where each bead carries a different structured ligand. These compounds have been at the basis of the selection of ligands to a particular target protein. By incubating these so-called one-bead–one-ligand © 2012 Taylor & Francis Group, LLC

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Mixed Beds

Phe

Lys

Ile Tyr

Arg

1 Incubate peptide library with the protein mixture

2 Identify beads capturing the target protein

3 Isolate positive beads and desorb the proteins

Gly Glu

4 Sequence the peptide ligand

Figure 1.9  (See color insert.) General principle to identify affinity ligands from a large library. 1: The library beads are incubated with the biological sample; when present, specific ligands interact with partner proteins and others are washed out. 2: Positive ligand beads for the target proteins are revealed with the help of specific markers and then isolated mechanically. 3: The adsorbed proteins are eluted using appropriate stripping agents and washed well. 4: The beads supporting the peptide are analyzed and the peptide sequenced. For methodological approaches, see corresponding text.

libraries with a purified tagged-target protein, bead ligands can be isolated and their molecular sequence identified (Figure 1.9). This approach is an efficient procedure for the identification of chromatographic ligands. This procedure involves the advantage of using solid beads; a ligand that binds specifically a target protein in solution might not be a good one after coupling on a solid support. This is mainly due to the influence of both the bead substrate that enhances or antagonizes the interaction and the modification of the ligand itself upon the chemical grafting operation. Mixed beds produced as combinatorial solid-phase ligand libraries comprising millions of diverse ligands can be screened in a few days with a high rate of technical success. The use of these libraries can be operated not only with the use of purified target proteins, but interestingly by using the initial crude biological material. The advantage here is to ignore all situations where the target protein competes with other molecules for the same ligand. Nevertheless, false positive beads could still be a problem that could be circumvented by some technical proposed approaches. One of them is to isolate the first positive beads from the screening step and rescreen under certain conditions. Other methods to resolve false positives have also been suggested, such as double staining or second incubation against a large variety of protein mixtures (Lam et al. 1995b; Buettner et al. 1996). However, in practice it is hard to eliminate all false-positive situations. In spite of some open issues, combinations of amino acids under short peptide chains probably represent one of the most powerful sources of affinity ligands for chromatographic separation. Amino acids carry chemical functions displaying various interaction forces. The most common are ionic charges (cationic and anionic), hydrophobic sited (aliphatic and aromatic) heterocycles, hydrogen bonding centers, and a number of other weak-force interaction points. Moreover, these combinations generate species with a well-defined isoelectric point and hydrophobic index facilitating the optimization of elution conditions. With the use of 20 amino acids a combinatorial library of hexapeptides gives up to 64 million individual diverse ligands © 2012 Taylor & Francis Group, LLC

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with consequently as many diverse effects with respect to interaction possibilities with protein epitopes. Combinatorial peptide libraries were first described at the end of the eighties in the last century, when Furka et al. (1988) presented the principle of synthesis as a way to simplify the preparation of peptides. It was about the same time when combinatorial chemistry became popular as a source of new molecules to screen for pharmaceutical applications. It was with Lam et al. (1991) that peptides from combinatorial libraries were applied for the first time as a possible source of affinity ligands for the separation of proteins from complex mixtures. A number of examples are reported in the literature for the identification of affinity peptides for protein separation (Kaufman et al. 2002; Samson et al. 1995; Lam, Lebl, and Krchnàk 1997; M. Pennington, Lam, and Cress 1996), such as, for example, human a-1-proteinase inhibitor (Bastek et al. 2000), the altered conformation of prion protein (Lathrop, Fijalkowska, and Hammond 2007), and groups of fusion proteins sharing the same tag directly from a crude extract in the presence of strong denaturing chaotropic agents (Hahn et al. 2010). Table 1.2 summarizes some described proteins specific for peptide ligands discovered from combinatorial libraries. Various methods have been described for the screening of solid-phase mixed-bed ligand libraries with the aim of identifying specific ligands. A number of ligand bead selection methods have been described over time. They have been improved progressively in view of reducing the number of false-positive responses. The methods Table 1.2 Identified Affinity Peptide from Combinatorial Libraries for Purification of Targeted Proteins Protein

Selected Affinity Peptides

Ref.

Streptavidin p60(c-src) tyrosine kinase Melanoma MSH receptors antagonist Glycosomal phosphoglycerate kinase Ribonuclease S Von Willebrand factor Alpha-6-b-1-integrin Coagulation factor IX Alpha-1-proteinase inhibitor Fibrinogen Staphylococcal enterotoxin B Fc region of human IgG Anti-insulin antibodies Prion protein Alpha-amylase Beta actin Alpha-n-b-3 integrin

IQHPQ YIYGSFK WRL NWMMF YNFEVL RVRSFY LNIVS-VNGRHX YANKGY RAFWYI FLLVPL YYWLHH HWRGWV EFDWNH GLERPE FHENWS Various RGD

Lam et al. 1991 Lam et al. 1995b Quillan, Jayawickreme, and Lerner 1995 Samson et al. 1995 Buettner et al. 1996 P. Huang et al. 1996 M. Pennington et al. 1996 Buettner et al. 1996 Bastek et al. 2000 Kaufman et al. 2002 Wang et al. 2004 Yang et al. 2005 Lehman et al. 2006 Lathrop et al. 2007 F. Liu et al. 2007 Miyamoto et al. 2008 Xiao et al. 2010

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described used purified targets as well as crude protein extracts containing or not containing the target protein in order to make comparisons and deduce rational responses. In practice the protein mixture is incubated with the mixed-bed ligand library and, after incubation, the bead bed is washed extensively to eliminate the excess of proteins along with proteins that did not find their partner peptide. Then the protein-loaded beads are incubated with an antibody against the target protein and positive beads revealed by immunostaining. However, the direct interaction between the antibody and peptide ligands or between the antibody and the bead chemical matrix can generate many false positives. Stringent conditions of capturing may contribute to reduce nonspecific binding and hence false positives: however, the question remains largely open. In addition, to find optimized conditions of protein capturing for the target molecule, elution conditions need also to be checked in order to be compatible with normal exploitation situations. It happens, in fact, that the interaction of a protein with a given ligand could be so strong and specific that the elution becomes a real challenge without the denaturation of the target protein. It is in this context that variations to the principle have been made to optimize all the processes. Improvements have also been made in order to increase the throughput of screening and ligand identification methods. The most well-known ligand identification methods involving mixed beds of immobilized peptides are briefly described next: • One of the described ligand bead screening methods detects directly the positive beads (Lam et al. 1991). The purified target molecule is coupled to an enzyme such as alkaline phosphatase or even to a fluorescent dye and then added to the mixed-bed ligand library. After several minutes of gentle shaking, the beads are washed to remove the excess of the target protein. Then the enzyme is incubated with its substrate to reveal the activity within the beads where the target molecule is captured. Alternatively the beads are observed under a UV light. Typically, as reported, few beads are well stained or detectable fluorescently. They are individually removed from the bulk bead library and washed with concentrated guanidine hydrochloride to desorb the target protein. The bead still carrying the peptide is finally analyzed to determine the sequence of the peptide. To decrease the number of false positives, optimization of the process has been made by Lebl et al. (1995). • A dual-color bead specific detection approach was proposed in order to reduce the number of beads that were to be decoded (Lam et al. 1995a). Here, the beads were first screened and labeled with one color and then by an orthogonal reagent with a second color substrate. This approach enabled elimination of a number of false-positive beads. • Buettner et al. (1996) subsequently reported another dual-color approach to screen their peptide bead libraries in view of discovering a peptide affinity ligand against human factor IX. The method consisted of multiple sequenced injections into HPLC library-packed columns alternated by immunostaining releasing two different colors. The first phase consisted of injecting the immunodetection system and stain positive beads in blue (BCIP/NBT substrate). Then, a second injection of the sample containing © 2012 Taylor & Francis Group, LLC

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the target protein followed by the immunodetection allowed sorting out other beads stained in red with another substrate. Although quite elaborate and necessitating programmed HPLC, this approach significantly reduced the number of false positives. Then the extracted beads were analyzed to sequence the affinity peptide. • In 2002, L. Liu, Marik, and Lam (2002) described the mass-tag encoding strategy for a small-molecule combinatorial library. The mass spectrometry isotope pattern of each tag could define the component building blocks of each selected bead within a quite limited library screened to find a ligand partner to streptavidin. The identification was performed by means of both enzyme-linked colorimetric assay and quantum dot/COPAS assays. Two years later, the same research team (Hwang et al. 2004) published a second method of encoding with the quantum dot/COPAS assay. This method offered some advantages over the prior one; however, it was relatively complicated to put in practice by common biochemistry laboratories. • To prevent the presence or to reduce the number of false positives, the strategy of using two protein mixtures as screening probes was described as the “image subtraction” approach (Lehman et al. 2006). Based on the optical image comparison of the beads stained by one protein mixture but not the other, selected ligand beads unique to one of the two protein mixtures could be identified. The main advantage of this procedure is the rapid selection of beads directed against proteins unique to one mixture and at the same time sorting out positive beads resulting from proteins common to both mixtures. Beads that were also positive due to their interactions with protein components found in the assay were eliminated. The method appeared quite efficient and far simpler than the tag encoding, with the advantage of using regular laboratory equipment. • Another selection method of bead ligands from a combinatorial library bed was performed using the so-called “bead-blot” method (Lathrop et al. 2007). Ligand beads after incubation with the crude sample and washing out the excess of proteins were embedded within a gel layer of agarose, forming a sort of bead array. The bound proteins subsequently were then transferred from the beads by capillary action in a manner similar to DNA transfer in a Southern blot and captured by a protein-binding membrane placed on top of the agarose gel layer. This way, the position of transferred proteins on the membrane reflected the position of the beads in the array. Subsequently, the membrane was probed for the target protein and, by its positioning on the membrane, the ligand bead was identified in the gel layer array. The bead was then isolated, the protein desorbed, and the peptide sequenced. This approach allowed identifying bead ligands for many proteins at a time simultaneously or sequentially. False positives are also largely reduced because the proteins are probed after diffusion on the membrane, as reported. Additional insights have recently been added by Maillard et al. (2009) with respect to the design of a peptide library, synthesis as well as the screening and characterization. © 2012 Taylor & Francis Group, LLC

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Bead decoding is another aspect to the success of ligand discovery. In the case of peptides, the amino acid composition is not enough; it is also necessary to know the exact sequence. Reported approaches are the determination of sequences by Edman degradation (Lam et al. 1991) or by mass spectrometry (Redman, Wilcoxen, and Ghadiri 2003).

1.6  Mixed Beds for Isoelectric Group Separation Fractionation of protein mixtures according to their isoelectric point is generally performed using pH gradients and under an electrical field (Righetti 1983, 1990). In other instances, chromatography could also be used by means of pH gradients that are self-arranged in chromatofocusing (Sluyterman and Elgetstha 1978). In this latter case, the solid bed is composed of homogeneous ion exchangers. Quite recently, with the use of mixed beds, it had been possible to perform fractionation by pI ranges using fixed beds and with no pH gradient (Fortis et al. 2005, 2008) as described next. Based on its composition, a protein is an ionizable macromolecule with a net charge depending on the environmental pH. The pH at which the net charge is zero is called the isoelectric point (pI); thus, the net charge of a protein becomes nil when the pH of the buffer where the protein is dissolved is the same as its pI. The protein is positively charged when the environmental pH is below the pI and is negatively charged when the pH is above the pI. When a protein mixture is loaded into a column of ion exchange packing, the pH of the buffer regulates the ionization of individual proteins. Species that have a net charge complementary to the ion exchange resin are captured while others remain in solution and are found in the flow-through. After washing, the captured proteins can then be eluted sequentially by a displacement salt-step gradient or a pH gradient. Proteins of the flow-through could possibly be refractionated in a second ion exchange resin at a different pH, then in a third fractionation, and so on. Such an approach is labor intensive because it implies multiple reequilibration operations of nonretained proteins with buffers of different pH and because salts used for the protein elution must be removed by means of separate unitary operations such as diafiltration, dialysis, or gel filtration chromatography. In attempting to render the fractionation easier and performed under a column cascade, solid-state buffers have been recently developed. In the separation process, it was proposed to replace liquid buffers by “solid-state buffers.” They are discrete particles of amphoteric polymeric beads inducing predetermined environmental pH like liquid buffers. Solid-state buffers have thus been formulated to induce a variety of pH values between 3.6 and 10.3. To work under well-established pH conditions, they are blended with ion exchange resins to get a mixed-bed packing. Bead mixtures are then filled in distinct columns that are finally placed under a cascade configuration as schematically illustrated in Figure 1.10. If a cation exchanger is used throughout the sequence, the top sectional column contains the solid buffer of the highest pH value and the bottom sectional column contains the one with the lowest pH value. Conversely, when an anion exchange resin is used, solid buffers are aligned under a reversed pH sequence value. The protein mixture is as usual loaded at the top of the first column; proteins and small ions get in contact with the solid buffer © 2012 Taylor & Francis Group, LLC

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Egisto Boschetti and Pier Giorgio Righetti Proteins with pl > 6.2 Proteins with pl 6.2–5.4 Proteins with pl 5.4–4.6 Proteins with pl < 4.6 SSB 6.2 + CEX

SSB 5.4 + CEX

SSB 4.6 + CEX

Figure 1.10  (See color insert.) Schematic representation of protein separation by isoelectric point groups using a sequence of mixed beds constituted of solid-state buffers (SSBs) and ion exchangers. The mixed beds are here constituted of a cation exchanger (CEX) and the pH of solid-state buffers aligned are, as indicated, between 6.2 and 4.6. Basically, the protein solution (here represented by four pictograms) is injected in the column sequence; proteins of pI below 4.6 are found in the effluent of the last column since they do not acquire the right ionic charge to be captured; proteins above 6.2 and between 5.4 and 6.2 and between 4.6 and 5.4 are desorbed separately from each sectional column.

and a well-defined environmental pH is generated, thus influencing the net charge of proteins present in the mixture. Those having a net charge complementary to the ion exchange resin are captured and the others are progressively pushed in the second sectional column. Here, another solid buffer is present that induces another environmental pH, thus ionizing differently proteins coming from the first sectional columns. Again, species having a net charge opposite to the ion exchanger are captured and others are pushed into the third sectional column. These operations are repeated as the number of sectional columns increases. Once the fractionation mechanism is completed, the columns are separated from each other and the captured proteins from each column are desorbed by either a salt solution or a change in the pH by a strong liquid buffer. This mode of fractionating protein mixtures is effective if specific rules are followed:

1. The initial protein solution has to be in low ionic strength without buffering ions. 2. To prevent protein–protein interaction, non-ionic dissociating agents can be added. 3. Loading should not exceed the binding capacity of the individual sectional columns. 4. Washing performed with a solution of the same composition as the one where proteins are initially dissolved must be limited to the elimination of nonadsorbed proteins.

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To prevent a too large dilution of protein species that do not adsorb throughout the series of columns, a column filled with an ion exchanger resin of opposite sign could be placed at the bottom of the sequence. This mixed-mode chromatographic process for isoelectric fractionation has been used successfully for the separation of a large number of natural and artificial protein mixtures. Its interest is that it does not require amphoteric molecules such as soluble carrier ampholytes (Ampholine) and the separation time lasts for only a few dozen minutes. The number of pI fractions depends on the number of solid-state buffers used and hence on the number of sectional columns aligned. Figure 1.11 illustrates the fractionation of a crude protein extract of Escherihia coli in the acidic part of isoelectric points where the majority of proteins are present. It could be seen that groups of proteins could be obtained with a limited overlap. Due to the concentration effect of single sectional mixed beds, additional low-abundance proteins are detectable when compared to the initial control. Another benefit of this mixed-mode pI fractionation is that the initial sample does not need to be concentrated and by consequence large volumes are thus tolerated. Proteins are actually concentrated at each sectional column. All along the fractionation process, the presence of a certain level of ionic strength and the presence of urea as dissociating agent prevent possible precipitation of proteins at the vicinity of their isoelectric point.

pl < 4.6

Initial sample pl 4.6–5.4

pl 5.4–6.2

pl > 6.2

Figure 1.11  Two-dimensional electrophoresis (2-DE) analysis of protein fractions obtained upon separation of E. coli protein extract by isoelectric point groups using a mixed bed of cation exchanger and solid-state buffers of pH 4.6, 5.4, and 6.2. Window on the right is the initial unfractionated sample; all other images are related to each fraction as indicated. 2-DE analysis was performed using a nonlinear pI gradient between 3 and 10. © 2012 Taylor & Francis Group, LLC

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1.7  “ Blind” Protein Purification Processes with Mixed Beds The regular procedure for the purification of one protein from complex extracts by chromatography is mainly based on the principle of trials and errors involving orthogonal separation mechanisms such as ion exchange, hydrophobic, mixed-mode, affinity and reversed phase interactions. These approaches are labor intensive even for experienced people. The columns used are not always compatible with each other in terms of buffer composition, ionic strength, and pH; moreover, the desorption of the protein fraction containing the target protein may require a long optimization of elution gradients. The method described here involving mixed beds consists of a few standardized steps of sorbent selection and then media blends each time the buffer used for chromatography is of the same composition (L. Guerrier, Lomas, and Boschetti 2005). Initially, a protocol has been devised involving a series of interconnected columns capable of removing progressively, under a complementary manner, all or almost all impurities, leaving the last column to capture the target protein. From this principle, it was logical to mix sorbent together in a single column to simplify the process exploitation with a single injection and a single elution. In this respect, mixed beds would provide a simple way to capture at the same time a large number of proteins while leaving the protein to isolate in the flow-through. The issue to resolve is the proper selection of individual sorbents to accomplish the job: namely, chromatographic media for impurity capture and a sorbent for the capture of the target protein even if this latter sorbent would cocapture some impurities. As described (L. Guerrier and Boschetti 2007), the overall development for such a process is composed of three main steps, two of them operated concomitantly: (1) the selection of resins to capture, under complementary manner, most proteins but not the target one, (2) selection of at least one resin capable of capturing the target protein with the least number of other coadsorbed species, and (3) the definition of the resin blend for the elimination of the maximum number of impurities. The entire selection needs to be operated under the same physicochemical conditions of buffer, salinity, and pH. The mixed-bed sorbent is positioned as a first column and directly connected to a second column packed with the most selective sorbent for the target protein itself issued from a preliminary screening process. When the sample is loaded on the top of the first column, noninteracting proteins are eliminated in the flow-through (first contribution to impurity elimination). Other protein impurities are progressively removed by the mixed-mode bed (second contribution to the removal of impurities), while the target is captured by the second sectional column with a possible coadsorption of few other species. The proper elution of the target protein from the second sectional column with possibly an optimized gradient yields the purified target protein (third contribution to the elimination of protein impurities). The entire process is better illustrated and explained in the Figure 1.12 scheme. The selection of sorbents is generally random from a collection of the largest number of diverse chromatographic materials and could be performed in a 96-well filtration plate. As described, the plate could be divided into two, three, or even four © 2012 Taylor & Francis Group, LLC

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b

a

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h

d f

g

(a)

Impurity capture

Target protein capture

FT Additional impurities (b)

1

2

3

Wash out Elute Desorb coadsorbed target other impurities protein impurities (c)

Figure 1.12  (See color insert.) Process scheme to find appropriate chromatographic sorbents for the preparation of a mixed-bed column and its application to the separation of a given protein from a complex mixture. (a): A 96-well filtration plate where the selection of chromatographic material to capture impurities is operated (selected sorbents are here indicated from “a” to “g” and then used for the preparation of the bed blend). (b): The setup of two columns aligned for the separation process; the first column where the initial crude sample is injected is made by a blend of selected sorbents able to capture impurities; the second column is filled with a sorbent able to capture the target protein. Noncaptured protein impurities are found in the overall flow-through (FT). (c): The second column after dissociation from the setup from where the target protein is desorbed as a single fraction or by means of sequential solutions (1, 2, and 3), allowing the separation of additional coadsorbed impurity traces.

quadrants in order to multiply the screening for the best working buffer. The methodology extensively described in 2007 (Guerrier and Boschetti 2007) applied to the selection of best sorbents, best buffers, and optimized sorbent blends as detailed here in the following. Briefly, as an example, a 96-well filtration plate is divided into three equal areas of 32 wells each. Each well is filled with 50 μL of 32 different chromatographic materials selected on the basis of their complementary properties and variants. They are, for instance, cation and anion exchangers with weak and strong chemical groups; hydrophobic resins with a short, medium, and long hydrocarbon chain and with aromatic rings; all kinds of mixed-mode resins as described in © 2012 Taylor & Francis Group, LLC

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a previous section; dyes used for pseudo-affinity chromatography; immobilized amino acids; or short peptides. The first quadrant of resins is equilibrated with an acidic buffer such as, for instance, 100 mM sodium acetate buffer containing 150 mM NaCl; the second quadrant of resins is equilibrated with a neutral buffer such as a physiological phosphate pH 7 and the third quadrant of the resin equilibrated with an alkaline buffer such as, for instance, 100 mM Tris-HCl containing 150 mM NaCl, pH 8.5. The biological sample is also split into three parts and each one equilibrated with one of the buffers. Then aliquots of about 50 μg of sample proteins equilibrated with the acidic buffer are loaded into the wells equilibrated with the same buffer and the same operation is performed for the two other buffered samples. The entire plate is gently shaken for few dozen minutes and then filtered under vacuum so as to collect 96 nonadsorbed protein samples. Three consecutive washings with the compatible buffer selected for each well region are then necessary to remove all nonadsorbed material. Bound proteins are eluted in two steps with 50 μl of a mixture of 9 M urea containing 2% chaps and then with 2.4% ammonia in distilled water. All eluates are neutralized and stored in the cold along with nonadsorbed fractions for further analysis such as SDS-PAGE, two-dimensional electrophoresis, mass spectrometry, or HPLC. Data from each explored buffer are then to be processed manually or using dedicated programs in order to sort out chromatographic sorbents capable of capturing the target protein with the minimum number of impurities. Then, the same selection is to be made for sorbents capable of capturing protein impurities under a complementary manner. All of this latter series must not be able to capture the target protein. Naturally, this selection of sorbent is to be performed within the same buffer experiment: The best combination is selected within a same buffer. Once the chromatographic sorbents selection is complete, sorbents selected for the capture of critical impurities are mixed together in equal proportions and then the blend used to pack a column; the sorbent selected for the capture of the target protein is singularly packed in a second column. The columns are connected together and homogeneously equilibrated by flushing at least three volumes of the considered buffer. The crude protein mixture is loaded into the first sectional column of the tandem and pushed with the buffer. Once all protein excess is washed out (baseline of detection at 280 nm), the two columns are disconnected and separately eluted with a stripping solution such as 9 M urea, 2% chaps, and 2.4% ammonia, pH 11. When required, for a better purity of the target proteins captured by the second column, an optimization of the elution gradient could be carried out. Desorbed target proteins are generally at a good level of purity for further studies. This method applies to proteomics investigations when the identification of a mass spectrometry protein signal is required (Guerrier, Lomas, and Boschetti 2007; Guerrier et al. 2008). For instance it has effectively been used for the identification of several proteins such as transthyretin and PTF2 (Guerrier and Boschetti 2007), yeast-activating protein, DNA-binding protein HU and PTF1 (Guerrier et al. 2008), and transferrin (Guerrier, Lomas, and Boschetti 2007) (see two examples in Figure 1.13).

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Initial extract

1

2

3

4

1

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Crude extract

YAP-1 Dye 17 ligand Impurity Heparin ligand capture Dye-4 ligand PTH-F1

Dye-23 ligand

PTF-1

Additional impurities

MBI ligand Dye 9 ligand CM sorbent

Impurity capture

Heparin ligand

YAP-1

Additional impurities (a)

(b)

Figure 1.13  Examples of protein purification using sequences of two columns: mixed bed followed by a homogeneous bed. (a): Scheme of PTH-F1 (prothrombin fragment 1) separation of two sequential columns and SDS-PAGE analysis of obtained protein fractions. Components of the mixed-bed blend and of the second column were selected from a large collection of chromatographic sorbents. Lanes 2, 3, and 4 represent, respectively, the composition of the initial sample (serum fraction), the impurity captured by the mixed-bed column, and the final purified PTH-F1 desorbed from the second sectional column. (b): Separation process of a recombinant protein called YAP-1 (yeast activating protein) expressed in E. coli and electrophoresis analysis of separated fractions. Components of the mixed-bed blend and of the second column were selected from a large collection of chromatographic sorbents. Lanes 2, 3, and 4 represent, respectively, the composition of the initial sample (whole extract of recombinant E. coli), the impurity captured by the mixed-bed column, and the final purified YAP-1 desorbed from the second sectional column. Lanes 1 of both experiments represent the molecular mass ladder. Both protein purification processes were applied to the identification of the target protein by peptide mass fingerprint and peptide sequencing by mass spectrometry. (Adapted from Guerrier, L. et al. 2008. Journal of Proteomics 71:368–378.)

Although it could be used at a preparative level depending on the purity and recovery required, the process has been developed for proteomics studies. With appropriate analytical tools, the time required for the selection of sorbents and for the preparation of a mixed-mode column is a few days only.

1.8  The Place of Mixed-Mode Chromatography within a Protein Separation Scheme Protein purification starting from very crude extracts has been a challenging task for many years and still to date there are not precise processes to resolve all possible situations. The reason is because proteins to isolate are so diverse that there are not real models where it is possible to start from, except for groups of homogeneous species likewise antibodies. The number and the diversity of protein impurities are also extremely large, making a difficult task for each case. A variety of approaches has been suggested over the years; however, the rationalization of purification processes is still an enormous task. Would mixed-bed chromatography be contributing

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to facilitate the life of protein purification specialists? This is difficult to say and, even if it might be easy to imagine, it would not be the ultimate solution. From what has been developed in previous sections, several situations could be successfully resolved with the use of mixed beds: (1) Ligands specific for a given protein to purify could be sorted out from very large mixed-bed libraries, (2) groups of proteins could be obtained using beds of mixed sorbents sharing the same loading conditions, and (3) last impurity elimination could also be removed thanks to blended media. The latter methodology along with associated features and benefits is described next.

1.8.1  P  olishing Aspect or Removal of Impurity Traces from Purified Biologicals Most classical approaches for protein purification combine various fractionation steps. The first is classified as the “capture” step since it operates a more or less specific extraction of the target protein; the second is the “separation” step of main impurities, and the final step is named “polishing.” The latter is entitled to remove all minor residual protein impurities that are present in trace amounts. They can be originated from the host cell where the expression of the target protein takes place and/or from leached proteinaceous ligands from previous solid-phase fractionations and/or resulting from partial hydrolysis or partial protein aggregation generated during the downstream process. The literature is rich in describing combinations of chromatographic methods. Flow-sheeting tools for designing suitable combinations are available to date and computer programs have also been developed to help users (Österlund 1995). The situation is so complex, however, that polishing steps could advantageously be approached by statistical methods. One possible solution could come from ligand libraries. Combinatorial peptide ligand libraries or “mixed-mode, mixed-bed” packings have originally been developed as a means to reduce the concentration of high abundance proteins in a sample while concomitantly increasing the concentration of rare species in view of enlarging the possibility to in-depth deciphering proteomes (Thulasiraman et al. 2005), as described in Section 1.3. Considering that in protein purification the final stage consists in removing the last impurity traces, the latter could be assumed as being unknown low-abundance species like in proteomics investigations. Combinatorial ligand beads were thus considered as a possible tool for either enhancing the level of impurity concentration to better detect them or eliminating protein impurities in view of obtaining a further purified material. In this section, the second aspect—polishing—is considered. Contrary to the process of enhancing low-abundance proteins, here the sample to treat should not be used in overloading conditions, but rather in such amounts that the protein impurities do not completely saturate the partner beads (Figure  1.14). This approach has been experienced with interesting results. Mechanistically, when a purified protein still comprising impurity traces is loaded on a packed column of a mixed bed of combinatorial immobilized ligands, all proteins (the main one and the impurity traces) will interact with © 2012 Taylor & Francis Group, LLC

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Mixed Beds Removed impurities a

Pre-purified protein

Mixed-bed library treatment ‘‘Polished’’ protein b

c

Figure 1.14  Schematic representation of a generic polishing process (removal of impurity traces here indicated as “a,” “b,” and “c”) using a mixed-bed ligand library. The process is operated under nonsaturating conditions so as to capture most impurities while cocapturing only small traces of the main protein. Captured impurity species are then desorbed by stripping agents and the solid-phase library column reutilized for a second run.

their partner ligand bead and are thus subtracted from the solution. However, the main protein very rapidly saturates its partner ligand bead and will go to the flow-through alone. While continuing to load the sample to the mixed bed, the impurities will continue to be adsorbed up to the saturation. Since in polishing processes, impurities could, by definition, be very numerous or in trace amounts, they are subtracted from the main protein that continues to leave the column at better purity than what it was at the initial stage. When all ligand beads are saturated, the column flow-through and the loading have the same composition. To get a very pure target protein, it is thus essential to monitor the column effluent during this impurity stripping process and stop the polishing process when they start to appear in the flow-through. To illustrate the performance of the procedure, two examples are given. The first deals with the removal of E. coli protein contaminants spiked in a purified preparation of myoglobin, and the second example shows the removal of impurities from a real sample of recombinant albumin at a purity of about 95%. In the first case, as illustrated in Figure 1.15, myoglobin is totally cleaned from all added impurities with just one passage on a peptide library column. In a second case, human albumin, expressed in Pichia pastoris, was dissolved in a physiological buffer and loaded on a peptide library column (Fortis et al. 2006). The purity of albumin at the outlet of the column was monitored by SDS-PAGE and the operation stopped when impurities started to leach out (Figure 1.16). The obtained purity was reported to be close to 99%; after identification by mass spectrometry, impurities appeared to come partially from the degradation product of albumin itself due to the presence of yeast proteases and others from the host cell where albumin was expressed. Impurity analysis was possible because they were captured by the ligand library and thus largely concentrated and detectable for analysis, which was not the case before the polishing step. © 2012 Taylor & Francis Group, LLC

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pl

10

Myo

3

pl

10

250 200 100 75 50 37 25 20 15 10

Contaminants

3

pl

10

Treatment with peptide library Initial myoglobin

Polished myoglobin

Figure 1.15  (See color insert.) Two-dimensional electrophoresis analysis of an experiment of impurity removal from a contaminated myoglobin solution. Myoglobin was first contaminated with 5% (w/w) of E. coli soluble proteins and then submitted to a treatment with a peptide library under nonsaturating conditions. The treated myoglobin and the impurities captured by the beads were then analyzed separately. Polished solution of myoglobin showed a good degree of purity with few isoforms and dimer as usual. Three minor impurities remained in the solution, as shown by minor spots. (Adapted from Fortis, F. et al. 2006. Electrophoresis 27:3018–3027.)

These examples illustrate very well the capabilities of mixed ligand libraries for impurity removal. Although combinatorial solid-phase libraries as mixed-bed combinations of very many sorbents may represent a generalized solution, this approach suffers from a couple of weaknesses: (1) it may comprise capturing beads recognizing the target proteins with some consequent losses, and (2) it may comprise a large number of ligand beads that are not effective in recognizing protein impurities. Although these two limitations may reduce the efficacy of the process, the users of generalized combinatorial ligands do not need to spend efforts in selecting the most appropriate media. Due to the complexity of biological extracts, the use of a combinatorial library of ligands may not resolve all possible situations. Instead, an efficient means to proceed would be the use of polishing mixed-mode sorbents specifically selected for the case to resolve. Nonetheless, impurities are by definition a very heterogeneous group of proteins with different sizes; isoelectric points ranging from acidic to alkaline; various hydrophobic indexes; and, for mammalian proteins, different post-translation modifications. In this situation, defining a media blend addressing all impurities is a challenging task. In spite of these criticisms, mixed beds of specifically selected ligands for a given polishing purpose are also a possible approach. To this end, the solid-phase media used for the preparation of mixed beds are sorted out from the largest number of available chromatographic sorbents. This approach resembles the one described in Section 1.7, where the first step in fact addresses the capture of impurities. In spite of the additional workload of selecting individual media addressing already detectable © 2012 Taylor & Francis Group, LLC

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pH 8

A 280 nm

2

a

6 1

4

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2 0 0

5

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15

Min

45

50

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60

Figure 1.16  (See color insert.) Polishing experiment with recombinant human albumin expressed in P. pastoris. The purified albumin solution, still containing impurity traces, was injected into a chromatographic mixed-bed column of combinatorial ligand library and the effluent continuously monitored by SDS-PAGE. The impurity capture was performed in a phosphate buffered saline. The first part of the column effluent showed a good purity as monitored (electrophoresis lane on the left). At the end of the experiment, the column was saturated of impurities and the effluent purity was the same as the initial sample (electrophoresis on the middle). Impurities were then desorbed by using an acidic solution of urea and the eluate appeared as comprising almost only impurities (SDS-PAGE image on the right). (a): Washing step with the PBS buffer alone; (b): initial point of the desorption solution injection. (From Fortis, F. et al. 2006. Electrophoresis 27:3018–3027. With permission.)

impurities, the resulting process would be more efficient because the sorbent blend would comprise only sorbents for the capture of the targeted impurities.

1.8.2  Selection of Media for Mixed Beds Media selection in view of preparing mixed beds applies only when individual media behavior against target proteins and/or protein impurities is not known. This falls in the situation described in Section 1.7. Criteria to select sorbents are not only focused on recognition of the target protein or other proteins, but also on the conditions of exploitation. Actually, individual components of mixed beds need to work necessarily under identical conditions at least during loading; they must maintain their intrinsic properties all along the process. Regeneration conditions are also to be considered because after a full separation cycle, they have to be cleaned and the cleaning solutions have to be equally effective on each component of the solid-phase blend. © 2012 Taylor & Francis Group, LLC

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Individual binding capacity of beads is determined before blending. This is an important point to consider when making resin blends since binding capacity for a given volume of blend packing generally dictates the proportion of each component of the mixed bed. Determining the proper media selection and best conditions of work for all individual bed components is generally performed at a small or even very small scale with the real sample. In practice, a 96-well filtration plate allows exploring a large number of conditions; then, a simple SDS-PAGE generally results in composition of blends that are by definition different from one case to another. Main applications of resulting mixed beds are protein group separations or polishing steps intended to achieve the final purification stage.

1.8.3  Streamlining Single-Bed with Mixed-Bed Chromatography Although mixed-bed chromatography is probably not the solution to all protein separation problems, it may contribute to rendering the approach more rational. If one admits that a separation process constitutes three main phases—namely, capture, separation, and polishing—two of them could use mixed beds during the development or as a chromatography step itself. The capture step involves the use of selective ligands for the target protein; however, except for a few examples—for instance, antibodies captured by immobilized protein A—there is a quite limited number of ligands that can do a proper job for the specific capture of other proteins. When the ligand is not known, mixedbed libraries of ligands represent a possible way to discover the appropriate ligand structure with the proper affinity constant. The selection could be performed in order to have elution conditions compatible either with the nature of the sample (Hahn et al. 2010) or with the following separation column, thus preventing reequilibrating the resulting protein solution to another buffer for the second chromatography column separation. Most generally, the second separation phase is based on columns made of homogeneous beds. They are ion exchangers or hydrophobic sorbents or other “orthogonal” solid-phase material. They adsorb the target protein under conditions that leave many other components to go in the flow-through. In addition, the elution of the target protein can also be performed in such a way as to be as selective as possible. This leaves many proteins adsorbed that are eliminated later during the regeneration stage. The third step, used as negative chromatography configuration, is in charge of removing all trace impurities that still remain in the purified target protein. Impurities are not only proteinaceous hydrolysis products, but also unwanted aggregates or even host cell proteins present in trace amounts. The use of customized mixed-mode sorbent beds or random mixed-mode ligand libraries is desirable here. The losses related to the use of such columns are very limited and depend very much on the number and the amount of impurities to be removed. Best efficacy of this approach is when the impurity traces represent overall a few percentage of proteins and are composed of dozens if not more protein impurity species.

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Mixed beds of combinatorial libraries do not necessarily need to be used under prespecified physicochemical conditions (pH, ionic strength, or buffer composition). They accommodate very well with the conditions that are those of the elution of the preceding column. Actually the spectrum of interactions is so large that affinity of a given ligand for a partner protein is always found, providing the pH conditions stay within a reasonable range—say, between pH 4 and 9—even under chaotropic conditions (Hahn et al. 2010). Mixed-bed libraries of ligands are generally expensive, but they have the advantage of not necessitating a stringent development and are used as small columns since impurities to capture are very minor proteins at this purification stage.

1.9  Conclusion Mixed-bed chromatography resulting from the blend of two or more solid-state media represents a peculiar aspect of liquid chromatography for proteins and peptides. Although as a first approach, the blend of different media appears not to make sense, there are numerous applications where mixed beds simplify significantly the process of separation. Each component of the media blend is entitled to interact with one or a group of proteins of the mixture when the physicochemical conditions of loading are the same. Therefore, instead of using several columns, only one is operated. Elution of proteins could be performed en mass or sequentially using specific displacers against each component of the bead mixture. Removal of selected categories of proteins from a complex mixture is a clear example of success where mixed beds of immobilized antibodies are used together with consequent time saving and process simplicity. The mixed-bed technology today is only at its initial development and it is essentially adopted to resolve some situations in proteomic investigations. In this domain, there are still development opportunities for devising methods for the separation of protein groups such as those represented by the numerous posttranslational modifications beyond the described glycoproteins fractionation for proteomics and diagnostic investigations. Nevertheless, some preparative applications are also expected. One of them is the discovery of specific ligands for affinity chromatography that would facilitate the initial capture of targeted proteins from crude feedstock. Libraries of peptides, of chemical ligands as well as of oligonucleotides are available to apply methods for ligand selection. The process allows choosing the right affinity constant for adsorption–desorption operations, on one hand, and detect ligands that capture the target proteins under nonconventional conditions such as in chaotropic conditions or in conditions that are those of the initial protein extract, on the other hand. In addition, ligands capable of releasing the captured proteins under conditions compatible with following columns are also possible. Removal of protein impurities at intermediate purification stage and at final polishing stage is also a great strength of the mixed-mode chromatography process using either ligand libraries or rational media blend.

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Perhaps the most advanced field drawing the largest number of research efforts, where mixed-mode chromatographic approaches with combinatorial ligand libraries are used, is biomarker discovery. The probable reason is the fact that no novel clinical chemistry tests have been approved since the late sixties of the last century (the other reason is, of course, the romantic dream of hitting the pot of gold and being rewarded with decent royalties on the patents issued from such discoveries). Those “Forty-niners” might be quite disappointed: The literature is littered with hundreds and hundreds of initial reports on biomarker discoveries that have failed to reach the clinic. We are aware of only one successful enterprise: In November 2009 the FDA approved a new test for ovarian cancer: the OVA1. It took 7 years of hard work to get there! This study, utilizing SELDI technology, involved multi-institutional analyses encompassing more than 600 individuals. The test in current use (cancer antigen 125, CA125) did not have the ability to discriminate between malignant and benign ovarian tumors and did not permit detection of early-stage ovarian cancer. The novel OVA1 test that was approved exploits a panel of seven markers: ITIH4 (inter-a-trypsin inhibitor heavy chain 4), transthyretin, apolipoprotein A1, hepcidin, β2-microglobulin, transferring, and CTAP3 (connective tissue activating peptide III), in combination with the old CA125 test (and is currently the only one ensuring close to 100% sensitivity coupled to 100% specificity). This interesting story can be read in Fung (2010). But there is more to it; as we mentioned in Section 1.4.1, Tu et al. (2010) reported that biomarker discovery in sera (or plasma) immunodepleted (as in current vogue today) might lead nowhere, considering that the increase in identified proteins as compared to nontreated samples is barley 25%. Should we give up any hope, then? Perhaps not. As stated in this review, combinatorial peptide ligand libraries might just do that—that is, mine for the invisible and submerged proteome. We have already amply dissected that in previous sections and given most convincing evidence in Figure 1.5: In all cases investigated, it was possible to detect from 100% to 500% more proteins (i.e., up to 10–20 times as many as could possibly be discovered via immunodepletion). Thus, any chance for biomarker discovery would have to lean heavily on the mixed-bed technology with a peptide ligand library in future research and it can be predicted that such methodology as it is or after optimization will be amply adopted in the near future.

Acknowledgments PGR is supported by Fondazione Cariplo (Milano) with a 3-year grant for developing novel combinatorial ligand libraries.

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Peirce, M. J., Begum, S., Saklatvala, J., Cope, A. P., Wait, R. 2005. Two-stage affinity purification for inducibly phosphorylated membrane proteins. Proteomics 5:2417–2421. Pennington, C., Chohan, G., Mackenzie, J., Andrews, M., Will, R., Knight, R., Green, A. 2009. The role of cerebrospinal fluid proteins as early diagnostic markers for sporadic Creutzfeldt–Jakob disease. Neuroscience Letters 455:56–59. Pennington, M. E., Lam, K. S., Cress, A. E. 1996. The use of a combinatorial library method to isolate human tumor cell adhesion eptides. Molecular Diversity 2:19–28. Pieper, R., Gatlin, C. L., Makusky, A. J., et al. 2003. The human serum proteome: Display of nearly 3700 chromatographically separated protein spots on two-dimensional electrophoresis gels and identification of 325 distinct proteins. Proteomics 3:1345–1364. Pieper, R., Su, Q., Gatlin, C. L., Huang, S. T., Anderson, N. L., Steiner, S. 2003. Multicomponent immunoaffinity subtraction chromatography: An innovative step towards a comprehensive survey of the human plasma proteome. Proteomics 3:422–432. Porath, J., Oscarsson, S. 1988. A new kind of thiophilic electron donor–acceptor adsorbents. Macromolecular Symposia 17:359–371. Quillan, J. M., Jayawickreme, C. K., Lerner, M. R. 1995. Combinatorial diffusion assay used to identify topically active melanocyte-stimulating hormone receptor antagonists. Proceedings of National Academy of Sciences USA 92:2894–2898. Ranjini, S. S., Bimal, D., Dhivya, A. P., Vijiyalakshmi, M. A. 2010. Study of the mechanism of interaction of antibody (IgG) on two mixed mode sorbents. Journal of Chromatography B 878:1031–1037. Redman, J. E., Wilcoxen, K. M., Ghadiri, M. R. 2003. Automated mass spectrometric sequence determination of cyclic peptide library members. Journal of Combinatorial Chemistry 5:33–40. Regnault, V., Rivat, C., Vallar, L., Stoltz, J. F. 1992. Dye-affinity purification of transthyretin from an unexploited by-product of human plasma chromatographic fractionation. Journal of Chromatography 576:87–93. Righetti, P. G. 1983. Isoelectric Focusing: Theory, Methodology and Applications, 1–386. Amsterdam: Elsevier. ———. 1990. Immobilized pH Gradients: Theory and Methodology, 1–397. Amsterdam: Elsevier. Righetti, P. G., Boschetti, E. 2007. Sherlock Holmes and the proteome—A detective story. FEBS Journal 274:897–905. ———. 2009. The art of observing rare protein species with peptide libraries. Proteomics 9:1492–1510. Righetti, P. G., Boschetti, E., Kravchuk, A., Fasoli, E. 2010a. The proteome buccaneers: How to unearth your treasure chest via combinatorial peptide ligand libraries. Expert Review of Proteomics 7:373–385. Righetti, P. G., Boschetti, E., Lomas, L., Citterio, A. 2006. Protein equalizer technology: The quest for a “democratic proteome.” Proteomics 6:3980–3992. Righetti, P. G., Boschetti, E., Zanella, A., Fasoli, E., Citterio A. 2010b. Plucking, pillaging and plundering proteomes with combinatorial peptide ligand libraries. Journal of Chromatography A 1217:893–900. Roque, A. C., Gupta, G., Lowe, C. R. 2005. Design, synthesis, and screening of biomimetic ligands for affinity chromatography. Methods in Molecular Biology 310:43–62. Ross, C. A., Pickart, C. M. 2004. The ubiquitin-proteasome pathway in Parkinson’s disease and other neurodegenerative diseases. Trends in Cell Biology 14:703–711. Roux-Dalvai, F., Gonzalez de Peredo, A., et al. 2008. Extensive analysis of the cytoplasmic proteome of human erythrocytes using the peptide ligand library technology and advanced mass spectrometry. Molecular and Cell Proteomics 7:2254–2269. Samson, I., Kerremans, L., Rozenski, J., et al. 1995. Identification of a peptide inhibitor against glycosomal phosphoglycerate kinase of Trypanosoma brucei by a synthetic peptide library approach. Bioorganic and Medicinal Chemistry 3:257–265. © 2012 Taylor & Francis Group, LLC

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Mechanistic Studies of Chiral Discrimination in Polysaccharide Phases Hung-Wei Tsui, Rahul B. Kasat, Elias I. Franses, and Nien-Hwa Linda Wang

Contents 2.1 Introduction..................................................................................................... 48 2.1.1 Importance of Polysaccharide Phases in Chiral Separations.............. 48 2.1.2 Needs, Challenges, and Objectives...................................................... 50 2.1.3 Research Strategies.............................................................................. 53 2.1.4 Overview of Section Organization...................................................... 55 2.2 Key Principles and Details of Methods Used.................................................. 55 2.2.1 Chromatography.................................................................................. 55 2.2.2 Infrared (IR) and Circular Dichroism (CD) Vibrational Spectroscopies..................................................................................... 56 2.2.3 X-ray Diffraction (XRD)..................................................................... 59 2.2.4 NMR Spectroscopy: Liquid State and Solid State.............................. 59 2.2.4.1 Liquid-State NMR: COSY and NOESY.............................. 59 2.2.4.2 Solid-State NMR: MAS and CPMAS.................................. 61 2.2.5 Molecular Simulations: Molecular Mechanics, Molecular Dynamics, and Density Functional Theory or Quantum Chemical Simulations.......................................................................... 62 2.3 Microstructures and Chiral Cavity Structures of Dry PS Sorbents................ 62 2.4 Interactions of Sorbents with Solvents and Simple Nonchiral Solutes............ 67 2.5 Interactions of PS Sorbents with Chiral Solutes.............................................. 73 2.5.1 Overview.............................................................................................. 73 2.5.2 Effect of Solute and Sorbent Structure on Enantioselectivity............. 74 2.5.2.1 Results of PPA with Three Sorbents..................................... 74 2.5.2.2 Results on Structurally Similar Compounds with CDMPC or ADMPC............................................................. 79 2.5.2.3 Other Literature Results........................................................80 2.5.3 Summary of Mechanisms and Methods..............................................84 2.6 Conclusions and Outlook................................................................................. 85 Acknowledgments..................................................................................................... 85 List of Acronyms and Some Symbols....................................................................... 86 References................................................................................................................. 86 47 © 2012 Taylor & Francis Group, LLC

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2.1  Introduction 2.1.1  Importance of Polysaccharide Phases in Chiral Separations Many biomolecules—nucleic acids, proteins, polysaccharides, lipids, and many drug molecules—are chiral enantiomers, or stereoisomers that are mirror images of each other (Pasteur 1901; Schaus 2000; Caldwell 2001; Wainer 2001). A 50:50 mixture of chiral enantiomers is called a “racemate.” The enantiomers have identical physical and chemical properties. The human body contains, however, numerous chiral sites that show stereospecific interactions with only one enantiomer and may metabolize each enantiomer by separate pathways to produce different pharmacological activities. One enantiomer may be safe and therapeutically effective, while another may be toxic because of slow metabolism and accumulation in internal organs. Many drugs derived from natural products are enantiomers. As products of synthetic chemistry, many chiral drugs have been used as racemates until recent years. Examples include Prozac, used for treating depression, and Thalidomide—one enantiomer of which was found to be teratogenic to the offspring of some users. After 1992, FDA guidelines for racemate drugs required rigorous testing of each enantiomer for its pharmacological activity. There is a growing trend to develop single enantiomer drugs. In 2001, 69% of all newly licensed or late-stage development products were single enantiomers. Worldwide sales of single-enantiomer drugs exceeded $150 billion per year in 2002. Examples of single-enantiomer blockbuster drugs with 2002 sales of $1 billion to $8 billion are for cardiovascular (Lipitor, Zocor), depression (Paxil, Zoloft), gastrointestinal, and respiratory diseases. “Chiral switching” has been used by companies to maintain a competitive advantage (Rouhi 2004). To produce pure chiral enantiomers one needs to use enantiomer-specific synthesis or to produce a racemate mixture and separate the enantiomers. Significant advances have been made in the enantiomer-specific synthesis area; these will not be covered in this review. One racemate separation method, asymmetric crystallization, is often not feasible and cannot achieve a high yield (>90%). Adsorptive separations are generally applicable and can achieve high purity (>99%) and high yield (99%) if used in simulated moving bed (SMB) processes (Broughton and Gerhold 1961; Broughton 1984; Ganetsos and Barker 1993; Gattuso et al. 1996; Schulte et al. 1996; Francotte and Richert 1997; Miller et al. 1999; Juza, Mazzotti, and Morbidelli 2000; Huthmann and Juza 2002). For chiral molecules, “upstream processing” costs are 30% to 50% of the total production cost, and “downstream processing” costs (mainly separation and purification processes) are higher—50% to 70% of the total production cost (Agranat and Caner 1999; Srinivas, Barbhaiya, and Midha 2001; Agranat, Caner, and Caldwell 2002). The enantioselectivity, adsorption capacity (grams or moles sorbed per kilogram of sorbent), sorbent particle size, and column configuration are the four key elements that control the efficiency and cost of analytical and preparative chiral chromatography processes. The enantioselectivity of a sorbent, or the “enantioresolution” of the solute, is the ratio of the retention factors (k) or the equilibrium adsorption constants of the enantiomers (see Section 2.2.1). High enantioselectivity and moderate binding constants favor high productivity (measured as kilograms of product per kilogram

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of sorbent per day) and low solvent consumption (Francotte and Junkerbuchheit 1992; Thomas and Raymond 1998; Satinder 2000; Subramanian 2000; Franco and Minguillon 2001; Francotte 2001; Maier, Franco, and Lindner 2001). Chiral stationary phases (CSPs) with a small sorbent particle size (5–10 μm), for which high operating pressures (50–200 atm) are needed, have been used to reduce peak spreading (due to intraparticle diffusion) and to improve resolution in analytical chromatographic separations. CSPs with particle sizes of 20–30 μm have been used in preparative batch chromatography or in simulated moving bed (SMB) processes. The latter processes have an order of magnitude higher productivity and much lower solvent requirements than batch chromatography (Lee et al. 2005). Equipment costs are about 70% of the high-pressure SMB separation costs (ca. $100/kg). The Wang group at Purdue developed design methods based on the concepts of “standing concentration waves,” which can be used to help ensure high purity (99%) and high yield (99%) in medium- to low-pressure SMB processes (Ma and Wang 1997; Xie et al. 2000; Xie, Koo, and Wang 2001; Mun et al. 2003). These methods have been incorporated in a genetic algorithm program used to optimize particle size, column length, column configuration, and zone flow rates for SMB processes (Lee et al. 2005). Sufficiently high enantioselectivities are the key for the successful application of such methods. Many different types of chiral adsorbents—proteins, macrocyclic antibiotics, cyclodextrins, “Pirkle” phases (low molecular weight [MW] brush-type monolayers chemically attached to the particles’ surfaces), ligand exchange phases, and polysaccharide phases—have been developed over the past two decades (Pirkle 1997; Pirkle and Liu 1996; Snyder, Kirkland, and Glajch 1997). The key suppliers of these CSPs are the Daicel and Akzo Nobel companies. Derivatized-amylose or cellulose-based polymeric CSPs, or polysaccharide (PS)based phases, are quite effective CSPs. They have been used in over 50% of all analytical and preparative chiral separations of low molecular weight ( 1 or 0.8 or lower if S < 1. The higher the value of S is, the lower the solvent consumption requirements in an HPLC process are. To reduce solvent requirements, the k– and k+ values should preferably range between 2 and 10. For a given solute and sorbent, S may shift (a little or a lot) with changes in the solvent, or the solvent composition for mixed solvents (e.g., hexane–ethanol) and the temperature. To be able to fine-tune S, it is important to understand at a molecular level the sorbent–solvent and solvent–solute interactions. The sorbent particles in a column should be uniform in size, to the extent possible, to allow good packing that can withstand the high pressures used and can lead to reproducible flow patterns and stable column performance. The particles should have pore sizes as uniform as possible, to avoid asymmetric peaks, or peak tailing, due to diffusion delays in the smaller pores. The PS phases are loaded on the beads by using a strong solvent, which is removed by evaporation, allowing the formation of a thin film on the pore surfaces. The solubility of the PS phase in various solvents limits the range of solvents that may be used as mobile phases. To stabilize the column performance further and allow the use of strong solvents, the polymer may be cross-linked or be chemically attached to the pore surfaces (Ikai et al. 2008). Then, a polymer monolayer is used, with a thickness equal to a fraction of the polymer chain length. Only studies with nonchemically attached PS phases are reviewed here. The polymer film thicknesses typically range from 10 to 50 nm. Such films have properties similar or identical to those of the respective bulk solid polymer phase. The solutes and solvents must usually enter the polymer structure or be “absorbed” in the polymer phase, and they are not “adsorbed” only at the polymer film/solvent interface. After entering the bulk film structure, the absorbed solute or solvent molecules are adsorbed in the interior surfaces, on the polymer backbones, the side chains, or the nano-sized cavities found in the polymer structure.

2.2.2  Infrared (IR) and Circular Dichroism (CD) Vibrational Spectroscopies The infrared absorbance spectra of A(λ–1), where λ −1 ≡ ν is the wavenumber in reciprocal centimeters (cm–1) of the polymer sorbent, can be obtained by testing the loaded silica beads. Either the transmission mode (T-IR) or the diffuse reflectance mode (DR-IR) may be used. The spectra from the dry polymer are compared to those of polymer–solvent, polymer–solute, or polymer–solvent–solute mixtures to obtain evidence of relevant interactions from any observed spectral changes. If a peak of a polymer group vibration does not overlap with any peak of the solvent or the solute, then the spectral interpretation can be straightforward. Otherwise, difference spectra, of the spectrum of the sorbent plus the solute minus the spectrum of the © 2012 Taylor & Francis Group, LLC

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sorbent, need to be obtained; this can possibly complicate the spectral interpretation (Kasat, Chin, et al. 2006). The polymer phases can also be examined separately from the sorbent beads as flat thin films (Kasat et al. 2007; Lammerhofer 2010). Such films are deposited on silicon or germanium wafers by simple coating methods (then they are called “cast films”) or by spin-coating methods, which can produce films of more uniform thickness. ATR (attenuated total reflection) IR spectra are obtained from films of thicknesses ranging from 1 to 20 μm. In this mode, only the bottom portion of a film at a thickness up to about 1 μm is probed by the IR beam because of the limited penetration depth of the “frustrated” electromagnetic wave (Bellamy 1975; Colthup, Daly, and Wiberley 1990; Harrick 1961). Spectra with films in contact with solvent or with solvent and solute, or in situ, can be obtained. In both the classical mechanical and the quantum mechanical descriptions of molecular vibrations, the frequency of the vibration is predicted to be proportional to the inverse of the square root of the reduced mass m of the vibrating entity. The reduced mass for a heteronuclear diatomic molecule or a functional group that has two atoms or groups of masses m A and mB is given by the formula 1/m  = 1/mA + 1/mB. When one of the two groups (e.g., group B) undergoing a stretching vibration is constrained by a hydrogen bond with another group, its effective mass mB increases, and the effective reduced mass m increases. Then the wave number decreases. The hydrogen bond can also change the effective reduced mass m for other vibrations in molecular groups that are close to and interact with the primary H-bonded group. For a bending vibration, by contrast, it is convenient to use a vibrating string model to describe the mechanism. In classical mechanics, the frequency of a vibrating string is proportional to T/µ , where T is the applied tension and μ is the mass of the string. Upon the formation of hydrogen bonds, the tension of the string increases relatively more than the mass μ. Then the frequency increases. This is the key reason why the wavenumber of a bending vibration often increases when the group is hydrogen bonded (Lewars 2003). An H-bond can change significantly the transient dipole moment of a group during the vibration. Since the infrared band intensity (measured by the peak height or the peak area) is proportional to this dipole moment (or, more accurately, to the derivative of the molecular dipole moment with respect to the normal coordinate), such an H-bond can affect significantly (by a factor of 2 to 10 or more) the IR band intensity. Hence, one may use information on both the band wavenumber and the band intensity to infer changes in certain H-bonding states. From these changes, one can infer changes in sorbent–solute or sorbent–solvent interactions. The IR spectra of the dry PS sorbents can be used to probe the primary and secondary structure of the polymer molecules. When an amide I band arises from a C = O group that is hydrogen-bonded with an NH group (the vibration of which contributes the most to an amide II band)—either intramolecularly (in the same polymer chain) or intermolecularly (between two or more chains)—the hydrogen bonding affects both the energetics (the energy or the wavenumber) and the intensity of the vibration. The bands of stretching vibrations (e.g., of the C = O group, the NH group, or the OH group) are shifted to lower wavenumbers (lower frequencies and © 2012 Taylor & Francis Group, LLC

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lower energies). The bands of bending vibrations (e.g., of the NH group) are shifted to higher wavenumbers, as explained previously. Wavenumber changes in the presence of solvents or solutes provide molecular evidence of specific sorbent–solvent or sorbent–solute interactions. Elucidating such interactions by probing the IR bands of the solvent or solute molecules is desirable, but it is often challenging experimentally when the bands overlap with those of the free solvent or solute. Density functional theory (DFT) simulations (see Section 2.2.5) can provide fairly accurate wavenumber and absorbance predictions, which may be used to establish the theoretical basis of such interactions. A new, powerful method—absolute configuration modulation infrared spectroscopy (ACMIS)—has been used recently (Wirz, Burgi, and Baiker 2003; Wirz et al. 2004). With this method, one may probe diastereomeric interactions of enantiomers with sorbents in the presence of solvents. By collecting time-resolved IR spectra as the relative concentrations of the enantiomers change periodically and demodulating the spectra (via a Fourier transform), one can obtain difference spectra with higher signal-to-noise ratio than is possible by using conventional IR spectroscopy. A potential relative disadvantage of the ACMIS method, however, is the higher complexity in both the instrumentation and the method interpretation. Because the solute–sorbent interactions vary by changing the relative concentration of each enantiomer periodically from 0% to 100%, the interactions can be detected from the spectral changes. In principle, bands of either sorbent or solute functional groups can be probed. When the sorbent–solute interactions involve a group in a chiral helical polymer chain (amylose or cellulose), the group vibration frequency and intensity are sensitive to whether the incident IR beam has a right-handed (RH) or a left-handed (LH) polarization, R or L. The absorbance difference for these two incident polarizations, ΔA ≡ A L –  A R, is called the “vibrational circular dichroism” (VCD) and was first measured in 1973. The difference depends on the absolute configuration of a molecule, and it can be used for obtaining molecular conformations, which may change upon interaction with a sorbent. Thus, the method can be used to probe stereospecific solute or sorbent conformations and solute–sorbent interactions. Such VCD IR spectra of PS phases were obtained recently and have provided valuable complementary information to that obtained from regular IR spectra (Ma et al. 2008, 2009). The VCD theory is much more complex than the IR theory because the quantity ΔA depends on both the dipole moment (which determines A L and A R) and the circular magnetic dipole moment. The relevant physical effect producing VCD is called the “Cotton effect” and involves “excitons,” which are mixed molecular states of two interacting molecular excitations. The excitons’ properties and the sign of ΔA depend also on the molecular handedness of a helical molecule and the overall configuration of the groups involved. Even though ΔA is a small fraction (10 –3 – 10 –4) of A L or A R , it can be measured readily with a commercially available instrument in which many spectra are added up and averaged for improving the signal-to-noise ratio. The interpretation of VCD spectra can be empirical or be based on DFT simulations. Typically, where one observes an IR band, one observes a VCD “couplet,” which is a combination of a positive peak with a negative peak at a lower wavenumber, © 2012 Taylor & Francis Group, LLC

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called “(+ –)” couplet or, conversely, a combination of a negative and a positive peak (– +). Based on data correlations and DFT for amide I couplets, a (+ –) couplet often indicates a left-handed helical structure and a (– +) couplet indicates a right-handed helical structure (Lipp and Nafie 1985; Ma et al. 2008). Other rules for interpreting VCD data may be discovered from DFT or from data correlations. By contrast to IR, the effects of H-bonds on the frequency and intensity of VCD couplets have not been analyzed quantitatively, to our knowledge. Nonetheless, combining IR with VCD tools promises to provide a powerful method for elucidating nanostructural details and specific interactions of functional groups.

2.2.3  X-ray Diffraction (XRD) Since many PS phases are crystalline or semicrystalline, XRD data can provide useful information on long-range order and molecular structure. Changes in the diffraction patterns with solvents and solutes provide clues to molecular interactions. No single-crystal XRD studies are available for PS phases used in chiral separations because of the difficulty in growing single crystals, probably due to the large molecular weight and complexity of the modified PS-based polymer molecules. Some XRD single-crystal studies of nonderivatized amylose and cellulose and of some simple derivatized PS polymers have provided useful information on the polymer helix structure and pitch and formed the basis of molecular models (Vogt and Zugenmaier 1983). XRD studies of polycrystalline or semicrystalline PS phases have provided some information on inter-rod distances and helical pitch lengths (Kasat et al. 2007; Kasat, Wang, et al. 2008; Keiderling 2002).

2.2.4  NMR Spectroscopy: Liquid State and Solid State 2.2.4.1  Liquid-State NMR: COSY and NOESY By using oligomers (of smaller MW than those of actual CSP polymers), which are soluble in a solvent such as chloroform, one may use standard one-dimensional 1H and 13C (or other nuclei) NMR spectroscopies to probe the structure of the polymer. Evidence of π – π or other hydrophobic interactions may be obtained from chemical shift changes. Evidence on the selective binding of a chiral enantiomer to the polymer in solution can be inferred from changes in the OH or NH proton chemical shifts due to hydrogen bonding. The binding constant and the stoichiometry of the polymer–solute complex can be determined. Changes in the chemical shifts of aromatic protons may be attributed to p-stacked groups or shielding effects by neighboring aromatic rings. Peak broadening effects may indicate slow exchange of a solute between bound and free states. Measurements of NMR spin-lattice relaxation times may also provide valuable information of group mobilities and can help to further elucidate binding phenomena or other interactions. Two-dimensional NMR techniques provide more detailed molecular information for mechanistic studies, as they may allow more reliable NMR peak assignments, and help determine the polymer primary structure and secondary molecular conformation. Intramolecular interactions among protons of the sorbent may facilitate the construction of accurate molecular models, which may be tested and combined © 2012 Taylor & Francis Group, LLC

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with information from XRD, as well as from IR or VCD. The NOESY (nuclear Overhauser enhancement spectroscopy) method involves a series of two-dimensional experiments designed, based on the pulse sequences used and the delays between the pulse sequences, to determine which peaks are coupled to each other. This allows one to infer which atoms may be in “close” proximity to other atoms and elucidate the polymer structure and polymer–solute binding (Yamamoto, Yashima, and Okamoto 2002; Yashima, Yamamoto, and Okamoto 1996). Another type of a two-dimensional method is homonuclear correlation spectroscopy (COSY), which can provide information on which hydrogen atoms are spin– spin coupled to each other. One can determine the relative proximity of atoms or the type and strength of chemical bonds between them. The structures of ADMPC and cellulose-based CSPs and the interactions with various chiral solutes were elucidated in a series of comprehensive studies by Okamoto and co-workers (Yamamoto et al. 2002; Yashima et al. 1996). A typical 1H NOESY spectrum for ADMPC in CDCl3 is shown in Figure 2.6. The figure shows cross-peaks for protons at distances of 4 Å or less. Interactions were inferred for the glucose– glucose region (Figure 2.6a), the NH of the carbonate group with the methyl on the phenyl group (2.6b), and the NH groups (2.6c, d). Assignments of protons in the CHCl3

6-Me 2, 3-Me

2, 3-NH

Glucose

6 3 12 5

6-NH (ppm)

TMS

4

0 1 2 A

3 4 5 6 7

B

8 D

9 9

8

C 7

6

4 5 (ppm)

3

2

1

0

Figure 2.6  500 MHz 1H-NMR NOESY spectrum of ADMPC at a mixing time of 50 ms in CDCl3 at 30°C; chemical shifts in parts per million. (Reprinted with permission from Yamamoto, C. et al., 2002, Journal of the American Chemical Society 124 (42): 12583– 12589, Figure 1.) © 2012 Taylor & Francis Group, LLC

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groups at the two, three, or six positions of a glucose unit were made accurately. Other 1H-NMR spectra provided detailed accounts of chemical shift changes attributable to specific interactions of the ADMPC oligomer with the chiral solutes. These studies provided valuable insights and the bases of several detailed molecular models. 2.2.4.2  Solid-State NMR: MAS and CPMAS Magnetic dipole–dipole interactions among nuclei tend to broaden the NMR peaks substantially. Fast molecular motion in low-viscosity liquid solutions sharpens the peaks, leading to well resolved NMR spectra. In a solid, low molecular mobilities cause substantial peak broadening and long spin-lattice relaxation times. Hence, peaks are normally not well resolved (or not observed at all) for the sorbent molecules or (with few exceptions) for the solutes or solvents absorbed in the polymeric phase. The technique of magic angle spinning (MAS)—of spinning a sample in the NMR spectrometer magnetic field at the magic angle (54.74°) at high frequencies (5,000 to 7,000 cycles per second, or hertz)—allows the effective elimination of the broadening effects of the magnetic dipole–dipole interactions. If, in addition, there is some molecular mobility resulting in modest values of spin relaxation times, then well resolved and sharp NMR peaks may be observed for the actual solid PS phases. The MAS technique is quite sensitive for either 1H or 13C NMR of the polymeric side chains when they have some molecular mobility. MAS can also probe mobility changes caused by interactions with solvent, solute, or both. The peaks of the backbone carbon or hydrogen atoms cannot normally be observed, even with the MAS method, because such molecular groups are quite immobile. By using the CPMAS pulse technique or “cross-polarization” in addition to MAS, the backbone peaks can be observed. This technique entails irradiating the 1H nuclei at their resonance frequency, whence the proton nuclei can transfer energy to the 13C nuclei and produce stronger 13C MAS peaks. This polarization is most efficient for relatively immobile groups. The technique is based on the static component of the 1H – 13C magnetic dipolar interactions. This component can result from a lack of motion or from nonrandom anisotropic motion. The CPMAS technique overcomes many problems of low sensitivity and long relaxation times of the MAS technique and yields peaks mostly of the backbone groups (Wenslow and Wang 2001; Wang and Wenslow 2003; Kasat, Zvinevich, et al. 2006), complementing the MAS technique. Using both techniques for a given system, one can determine changes in peak chemical shifts, widths, and intensities and probe changes in the mobilities of both the backbone and the side-chain atoms caused by the introduction of a solvent or a chiral solute. From such spectral features, one can probe H-bonding, π – π, and other interactions. In certain cases, broad peaks of certain polymer or solvent groups may split into multiple peaks, indicating changes in the polymer crystallinity, in the molecular mobility, or in both (Wenslow and Wang 2001). Resolving the causes of such splitting may involve using a combination of CPMAS (probes groups of lower mobility), MAS (probes groups of higher mobility), and XRD (probes crystallinity) (Kasat, Zvinevich, et al. 2006; Kasat et al. 2007). One may also use advanced DFT modeling of solid-state NMR spectra to elucidate these issues further. Overall, the liquid-state NMR methods can provide valuable information of specific interactions of chiral © 2012 Taylor & Francis Group, LLC

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solutes with individual polymers or oligomers in solution. The solid-state MAS and CPMAS NMR methods can provide such valuable information for mechanistic studies of actual PS phases used in practical separations.

2.2.5  Molecular Simulations: Molecular Mechanics, Molecular Dynamics, and Density Functional Theory or Quantum Chemical Simulations Density functional theory (DFT) can be used for simulating IR spectra fairly accurately. Vibrational frequencies predicted by DFT are used to interpret IR spectra. By choosing suitable and representative molecular models, the strength of H-bonds and their effects on vibrational frequencies may be predicted and understood better. DFT is a quantum mechanical theory describing the spatial distribution of the electron density of many electron systems. This is done by using “functionals” (functions of other functions) of the electron density without solving explicitly for the wavefunctions. There are various semiempirical choices of electron density functionals and different levels of theory. Applying DFT for simulations of molecular geometries and H-bonding strengths and for predicting IR spectra can help elucidate some mechanisms of molecular interactions. For a system of a polymeric sorbent and a solute containing a total of more than 100 atoms, DFT calculations are too time consuming and may become impractical. For this reason, DFT is used for simulating single chain interaction with a solute. Molecular mechanics (MM) calculations are much simpler and faster, but less accurate. In this method, atoms and molecules are treated as balls connected with strings. By choosing a suitable classical mechanical force field for describing interatomic and intermolecular interactions, parameters such as string constants and the size of balls are assigned. MM simulations can be used to calculate molecular geometries for large molecules or macromolecules quickly at near equilibrium by minimizing their energy. Kasat, Zvinevich, et al. (2006) and Ye et al. (2007) used 12-mer polymer rods with fourfold helical pitch obtained from XRD data to represent AD, AS, and CD polymer sorbents. By using DFT, the geometry of chiral solutes and of one sorbent side chain can be obtained. Then the molecular dynamics (MD) method, which considers classical forces among atoms and molecules, can be used to simulate polymer microstructures, including chiral cavities, and the interactions between the cavities and solutes or solvents. By combining MM with MD, one can probe the role of steric hindrance, H-bonding, and other interactions between the sorbent and the solute and evaluate their possible links to the retention factors and the enantioselectivity.

2.3  M  icrostructures and Chiral Cavity Structures of Dry PS Sorbents The helical conformation of the polymer backbone and the overall structures of the cavities are an important reference for the actual sorbent structures in the presence of the solvent (mobile phase) and the solutes. Vogt and Zugenmaier (1983, 1985) © 2012 Taylor & Francis Group, LLC

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have proposed a threefold (3/2) alpha (left-handed) helical conformation for cellulose tris (phenylcarbamates) and a fourfold alpha helical conformation for amylose tris (phenylcarbamates) (Kasat, Chin, et al. 2006; Kasat et al. 2007). Most of the dry structures are assumed to be left handed (alpha helical) or found to be left handed from VCD data consistently with molecular mechanics calculations (Lipp and Nafie 1985; Ma et al. 2008). The polymer films of ADMPC, CDMPC, and ASMBC showed some optical birefringence, indicating anisotropic structures. XRD results indicated some crystallinity or partial long-range order (Kasat et al. 2007). XRD data showed one broad peak with d-spacings of 15.5 ± 3.5Å (AD), 16.3 ± 4.5 Å (OD), and 14.1 ± 2.5Å (AS). These spacings were inferred to correspond to the repeat distance between the helical polymer chains (see also Figure 2.20). The lower spacing of AS compared to AD is evidently due to the smaller length of the AS side chain due to its nonplanar structure or to having a “kink” in its structure. No other information could be inferred from these polycrystalline XRD data, and no single-crystal specimens could be produced and probed. Additional information on the state of the side chains and their hydrogen bonding states was obtained from ATR-IR spectra of the dry polymers. Kasat et al. (2007) examined mainly the 1800–1500 cm–1 wavenumber region, in which there are bands from the C = O, NH, and phenyl groups, which were part of the chiral cavities (Figure  2.7). Two observed broad overlapping peaks (A, B) for the amide I bands (mostly due to the C = O stretch vibration) for the three polymers were assigned to weakly or strongly H-bonded C = O groups, respectively. It was recognized that each of the polymer peaks A and B was produced by a distribution of H-bonding strengths. Small differences observed in these bands were possibly due to the differences in the helical structures and the molecular environments of these polymers. The wavenumbers were higher for the ASMBC bands than for those of ADMPC. These differences were predicted fairly accurately by DFT simulations. The DFT-predicted bands for a single side chain were sharper because, in the actual polymer, there were H-bonds between the side chains and possibly between adjacent polymer molecules as well. The predicted and observed phenyl bands for ASMBC were quite weak since the instantaneous dipole moment was quite small because no polar group was directly connected to the phenyl ring (see Figure 2.1). Ma et al. (2008) reported the VCD spectra of ADMPC polymer in the dry film state and in CD2Cl2 solution. Weakly and strongly H-bonded C = O (amide I) VCD bands were observed (Figure 2.8) consistently with the IR results. Strong VCD peaks for the glycosidic bond bands in the 1200–900 cm–1 range were observed and analyzed, providing information on the backbone helicity. The authors observed (– +) VCD bands in the amide I region for CDMPC but a (+ –) couplet for ADMPC. The VCD spectra in the aromatic region (~1612 cm–1) showed a reverse pattern for ADMPC and CDMPC, possibly due to the differences in the conformations of the two polymer side chains. DFT calculations (with the B3LYP/6-21G* level of theory) for a single monomer were performed to simulate the VCD spectra. A CH3-phenyl H-bond was inferred only in ADMPC. Yamamoto and co-workers (2002) synthesized and studied several low-MW PS polymers that were soluble in organic solvents. With two-dimensional NOESY in © 2012 Taylor & Francis Group, LLC

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Ph

II

III

ADMPC

CDMPC

ADMPC/CDMPC, side chain, simulation ASMBC

ASMBC, side chain, simulation

1800

1700

1600 1500 1400 Wavenumber (cm–1)

1300

1200

Figure 2.7  IR spectra of ADMPC, CDMPC, and ASMBC. The amide I (mostly due to C=O stretching), amide II (mostly due to N-H bending), and amide III bands are shown, along with the phenyl region band. The DFT simulations of the side chains show sharp peaks because of the absence of H-bond effects. (Adapted from Kasat, R. B. et al., 2007, Biomacromolecules 8 (5): 1676–1685, Figure 3.)

20

Noise

∆A × 105

10

0

–10

–20

Amide II Amide I Type I

Amide III

Amide I Type II

C-O-C

VCD 1800

1600

1400

Wavenumber (cm–1)

1200

1000

Figure 2.8  VCD Spectra of ADMPC in dry film (shorter and broader peaks) and in solution in CD2 Cl2. (Reprinted with permission from Ma, S. L. et al., 2008, TetrahedronAsymmetry 19 (18): 2111–2114, Figure 2.) © 2012 Taylor & Francis Group, LLC

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liquid state NMR spectra and computer modeling, they determined the polymer structure in the dissolved state. Moreover, by dissolving also enantiomeric solutes that interacted with the polymer, they were able to elucidate the polymer–solute interactions and infer possible causes of enantioselectivity for the dissolved polymer and solute. The distances between the protons on adjacent glycose units were estimated (see Section 2.2.4.1). Three-dimensional distance and energy profiles for a polymer dimer in solution were plotted. A left-handed 4/3 helical structure for ADMPC was proposed (Yamamoto et al. 2002), consistent with the inference of Zugenmaier and Steinmeier (1986) for amylose triisobutyrate. Ye et al. (2007) extracted ADMPC from commercial polymer-coated beads with chloroform (CHCl3) and obtained 1H-NMR spectra of the polymer in the presence of ethanesulfonic acid. These spectra were broader than those of Yamamoto et al. (2002) because of slower molecular tumbling motion in the higher MW polymer. The NMR spectra of PS polymers dissolved in organic solvents may differ to a large extent from those of the solid polymer. The polymer conformation, polymer packing, and interpolymer chain interactions may be quite different in the solid state. Hence, solid-state NMR spectra can be quite valuable, even though they are more slowly obtained than liquid-state NMR spectra. VanderHart et al. (1996) and Sei et al. (1992) were apparently the first to use solid-state NMR to characterize cellulose triacetate PS materials. A significant solid-state NMR study was done on ADMPC coated on porous silica by Wenslow and Wang (2001). The CPMAS 13C spectrum in Figure 2.9 was the first to show both backbone and side chain carbon peaks for ADMPC. Only slight differences were observed in the spectra of ADMPC and of ADMPC with hexane, which apparently was not incorporated in the solid structure and CH3

C a-d C-2-6 C=O (a)

C-1

Hexanes (b) 150

100 (ppm)

50

0

Figure 2.9  13C CPMAS solid-state NMR spectra of dry ADMPC (a) and ADMPC flushed with hexane (b). (Reprinted with permission from Wenslow, R. M., and T. Wang, 2001, Analytical Chemistry 73 (17): 4190–4195, Figure 1.) © 2012 Taylor & Francis Group, LLC

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Hung-Wei Tsui, Rahul B. Kasat, Elias I. Franses, and Nien-Hwa Linda Wang C=O

Ph II-IV

C-1b

C-b

CH3

ADMPC

CDMPC

ASMBC

C=O Ph III-IV 160

140

120

C-1b 100

C-b 80 (ppm)

CH 60

CH3 40

20

0

Figure 2.10  13C CP/MAS solid-state NMR spectra of ADMPC, CDMPC, and ASMBC coated on silica beads. The backbone peaks C-1b and C-b are shown along with several sidechain peaks C=O, Ph, and CH3. (Adapted from Kasat, R. B. et al., 2007, Biomacromolecules 8 (5): 1676–1685, Figure 6.)

affected the polymer conformation slightly. Based on correlations developed by Gidley and Bociek (1988) between the chemical shifts of the C-1 carbon and the glucosidic torsion angles, Wenslow and Wang (2001) postulated a helical structure with less than sixfold screw axis symmetry. Kasat et al. (2007) compared the 13C CPMAS NMR spectra of CDMPC, ADMPC, and ASMBC on porous silica beads (Figure 2.10). The results were consistent with those of Wang and co-workers. The differences in the chemical shifts and the peak widths were attributed to differences in the polymer packing and in the intermolecular and intramolecular interactions. The DFT-predicted chemical shifts for the side chain of the polymer agreed fairly well with the data. The observed differences (~7 ppm) in the chemical shifts of the C-1 resonances of CDMPC and ADMPC indicated that the helicities in their polymer backbones were different. By contrast, the chemical shifts of the backbone resonances of ADMPC and ASMBC C-1b peaks differed by less than 1 ppm, indicating similar helicities. Based on the simulations and the data, it was inferred that CDMPC had a threefold helical conformation, while ADMPC and ASMBC had a fourfold helical conformation. These results are important in the subsequent MD-docking simulations. MAS spectra of the three polymers (Figure  2.11) did not show the backbone peaks. Only the phenyl, CH, and CH3 peaks of the side chains were resolved. This indicated that the side chains were much more mobile than the backbone. For this reason, in the MM and MD simulations, these authors calculated first the energyminimized structure of the backbone and then allowed the side chains to relax © 2012 Taylor & Francis Group, LLC

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Ph I

67

CH3

ADMPC

CDMPC

ASMBC Ph III 160

140

Ph I 120

100

CH 80 (ppm)

60

40

CH3 20

0

Figure 2.11  13C MAS solid-state NMR spectra of ADMPC, CDMPC, and ASMBC coated on silica beads. Only some side-chain peaks are shown. (Adapted from Kasat, R. B. et al., 2007, Biomacromolecules 8 (5): 1676–1685, Figure 7.)

with the backbone structure fixed. Overall, the CPMAS and MAS results provided information on the relative molecular mobilities and the crystallinities of the polymers. Using the dry polymer molecular-level information as a basis, these authors proceeded to elucidate further the effects of several solvents and chiral solutes on the structure and to generate insights on the mechanisms of chiral recognition. It is emphasized that the polymer structure may change significantly upon solvent absorption, especially when the hydrocarbon-based solvent is mixed with polar solvents (alcohols, etc.).

2.4  I nteractions of Sorbents with Solvents and Simple Nonchiral Solutes The choice of solvents (or “mobile phases”) affects substantially the retention factors and enantioselectivities (Aboul-Enein and Ali 2001; Lynam and Stringham 2006; Tachibana and Ohnishi 2001; Wang and Chen 1999). The mobile phase solvent should not dissolve the polymer sorbent or should be a “weak” solvent. If another “strong” solvent, such as THF (tetrahydrofuran) or DMAc (dimethyl acetamide), does dissolve the polymer material, then one may use a bulk film of a cross-linked (insoluble) polymer. If the polymer is not cross-linked and a strong solvent is used, then one needs to use a polymer monolayer chemically attached to the substrate (see Section 2.2.1). Although studies of such materials are not reviewed here, approaches for studying sorbent–solvent interactions similar to those for polymer films may be used. © 2012 Taylor & Francis Group, LLC

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Table 2.2 Potential Interactions of ADMPC with Solvents and Simple Solutes Solvents or Solutes

Type of Interaction

Bonding Pairs (Sorbent–Solute)

Alcohols, water Alcohols, water Amines Amines Pyridine Tetrahydrofuran Pyridine, tetrahydrofuran Aromatics Hydrocarbons Benzene, pyridine, THF, DEA, aniline

H-bond H-bond H-bond H-bond H-bond H-bond H-bond Hydrophobic Hydrophobic Dipole–dipole

C=O…HO NH…OH NH…NH HN ……H2N/HN NH…:N NH…:O C=O…HC Aromatic…aromatic Hydrocarbon…hydrocarbon Many

Adapted from Kasat, R. B., C. Y. Chin, et al., 2006, Adsorption—Journal of the International Adsorption Society 12 (5–6): 405–416, Table 1.

Commonly used mobile phase solvents include hydrocarbons (hexane, heptane, etc.), alcohols (methanol, ethanol, isopropyl alcohol [IPA], etc.), acetonitrile (ACN), and others. Binary mixtures of these liquids are used even more commonly. For example, a 90–10 vol% mixture of hexane/IPA allows one to have both a substantial solubility of slightly polar chiral solutes and a controlled modification on the sorbent structure by the solvent, but not any sorbent dissolution. The solutes can interact with the solvent with hydrophobic, π–π, or H-bonding interactions. The solvent can also interact substantially with the sorbent. Examples of possible interactions of ADMPC with solvents are shown in Table 2.2 (Kasat, Chin, et al. 2006). Studies of such interactions of solvents or simple nonchiral solutes with sorbents were done with various direct-probing physical techniques and led to improved understanding of the more complex sorbent–chiral–solute interactions. In a detailed example for ADMPC, Kasat, Chin, et al. (2006) and Kasat, Zvinevich, et al. (2006) studied the effect of solvent absorption on the IR, XRD, CPMAS, and MAS spectra (Figures 2.12–2.15 and Table 2.3). The details may be reviewed in the original papers. The results revealed significant changes in the hydrogen-bonding states of the amide I, II, and III infrared bands (Figure 2.12 and Table 2.3) the polymer crystallinity (XRD, Figure 2.13) the backbone crystallinity (CPMAS, Figure 2.14) the side chain mobility (MAS, Figure 2.15) DFT simulations of IR and NMR spectra allowed improved insights and helped develop hypotheses for various interactions. Overall, with the exception of pure hydrocarbon solvents, the solvents could significantly change the polymer nanostructures © 2012 Taylor & Francis Group, LLC

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Ph II

69

III

ADMPC-ACN

Absorption

ADMPC-IPA ADMPC -Ethanol ADMPC -Methanol ADMPC -Hexane ADMPC 3500

3000

2500 1800 Wavenumber (cm–1)

1500

1200

Figure 2.12 (See color insert.)  Effect of solvent absorption on the IR spectra of ADMPC. (Adapted from Kasat, R. B., Y. Zvinevich, et al., 2006, Journal of Physical Chemistry B 110 (29): 14114–14122, Figure 2.)

ADMPC-ACN ADMPC-IPA

cps

ADMPC-Ethanol ADMPC-Methanol ADMPC-Hexane ADMPC Dry ADMPC 3

4

5

6

7

2θ

8

9

10

11

12

Figure 2.13  Effect of solvent absorption on the XRD pattern of ADMPC. (Adapted from Kasat, R. B., Y. Zvinevich, et al., 2006, Journal of Physical Chemistry B 110 (29): 14114– 14122, Figure 5.) © 2012 Taylor & Francis Group, LLC

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A ADMPC-ACN(A) I

I E

ADMPC-IPA(I) E

ADMPC-Ethanol(E)

M

ADMPC-Methanol(M) H

H

ADMPC-Hexane(H)

Ph

200

150

Dry ADMPC 100

(ppm)

50

0

–50

Figure 2.14  Effect of solvent absorption on the CPMAS solid-state NMR spectra of ADMPC. (Adapted from Kasat, R. B., Y. Zvinevich, et al., 2006, Journal of Physical Chemistry B 110 (29): 14114–14122, Figure 6.)

ADMPC-ACN ADMPC-IPA ADMPC-Ethanol ADMPC-Methanol ADMPC-Hexane Dry ADMPC Ph IV III II I 200

150

100

CH3 (ppm)

50

0

–50

Figure 2.15(See color insert.)  Effect of solvent absorption on the MAS spectra of ADMPC. The sharp peaks are due to the free solvent. (Adapted from Kasat, R. B., Y. Zvinevich, et al., 2006, Journal of Physical Chemistry B 110 (29): 14114–14122, Figure 7.) © 2012 Taylor & Francis Group, LLC

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Table 2.3 Experimental and Predicted Wavenumber Shifts of IR Amide I and II Bands of ADMPC upon Absorption of Various Solvents Wavenumbers (cm–1) System

Bond pair

ADMPC side chain With 1-propanol With 1-propanol With benzene With DEA With heptane With heptane With pyridine With THF With THF

N/A C=O…HC NH…OH C=O…HC NH…NH C=O…HC NH…CH NH…N C=O…HC NH…O

ΔE (kcal/mol) N/A –4.27 –5.47 –0.88 –4.93 (< 0.5) (< 0.5) –5.12 –4.29 –7.95

H-bond Distance (Å)

H-bond Angle (˚)

C=O (Amide I)

NH (Amide II)

N/A 1.97 2.00 2.50 2.04 N/A N/A 2.05 2.50 1.95

N/A 168 158 179 176 N/A N/A 177 168 179

1717 1700 1721 1711 N/A 1716 1718 1708 1713 1710

1512 1515 1549 1513 N/A 1512 1511 1546 1513 1543

Adapted from Kasat, R. B., C. Y. Chin, et al., 2006, Adsorption–Journal of the International Adsorption Society 12 (5–6): 405–416, Table 3.

and the types of molecular environments in the sites or cavities, which affected the chiral recognition. Such changes should be taken into account in comparing the predicted and the measured enantioselectivities. The first solid-state NMR evidence supporting these inferences was reported by Wenslow and Wang (2001) and Wang and Wenslow (2003). Adding even 1% IPA in hexane (or hexane mixtures) could change the NMR backbone bands and the polymer crystallinity inferences substantially (Figure 2.16). Substantial effects of the percentage of ethanol in hexane on the sorbent microstructure as inferred from the VCD spectra were reported by Ma et al (2009). A typical result is shown in Figure 2.17. For certain compounds, the changes in the sorbent cavity structure could even lead to a reversal in the elution order of the chiral solutes. Certain possible changes in the helical structure of the polymer from left handed to right handed were also inferred. In addition to the structural studies, HPLC data were obtained for ADMPC with 15 solvents or simple nonchiral solutes, to understand the roles of specific functional groups on the retention factors (Table 2.4; Kasat, Zvinevich, et al. (2006) and Kasat et al. (2010). The data indicated that the OH and NH groups contributed to higher retention factors (k = 0.5–1.0) than the CH3 (k = 0) or the phenyl functional (k ~ 0.2) groups. The k values attributed to the OH or NH groups were on average four to five times higher than those of benzene, which may interact mainly with the PS phenyl functional groups. The CN groups of ACN and pyridine and the CO group of THF had similar contributions to the overall retention factors as the OH and NH groups. The retention factor is proportional to the adsorption equilibrium constant, © 2012 Taylor & Francis Group, LLC

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C=O

C 2-6

C-1

Hexanes

(b)

(c) IPA (d) C-2, 5 C-3

C-6

C-4

(e) 150

100 (ppm)

50

0

Figure 2.16  13C CPMAS spectra of ADMPC with (a) hexanes (a mixture of hexane isomers); (b) 0.2% IPA in hexanes; (c) 1% IPA; (d) 5% IPA; (e) 10% IPA. (Reprinted with permission from Wenslow, R. M., and T. Wang, 2001, Analytical Chemistry 73 (17): 4190– 4195, Figure 2.)

which is related to the adsorption free energy of interaction. The DFT-predicted interaction energies or the relative binding strengths of an AD side chain with the solutes showed similar qualitative trends to those of the retention factors. Similar results were obtained for CDMPC (Kasat, Wee, et al. 2008). HPLC results provide clues to possible molecular interactions. The IR and DFT results showed that the key binding sites of these polymers were the C=O and NH groups, which interacted with the H-bonding (OH and NH) and hydrophobic functional groups of the solvents and the simple solutes. The DFTpredicted IR wavenumber shifts due to H-bonding of the polymer C=O and NH groups with each solvent were found to be consistent with the IR data. DFT calculations were useful for ranking the H-binding strengths of the various functional groups. The DFT-predicted energies of the interactions between the functional groups of one polymer side chain—having C=O, NH, and phenyl groups but no H-bonds—and those of the solutes OH, NH, NH2, O, phenyl, and N provided deeper insights for rationalizing the retention factors. The XRD, VCD, and IR results showed that the polymer formed helical rods with intra-rod and inter-rod H-bonds, resulting in the formation of various nanometer-sized cavities between the polymer side chains and between the rods, respectively. The polymer rods were reorganized upon absorption of alcohols or ACN, and the repeat distances between the rods increased slightly with the increase in the size of the alcohol molecule.

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1712

ADMPC

∆A × 105

∆A × 105

Phenyl Amide II

1750 1720

Dry film 1% Ethanol 20% Ethanol

Amide I

–15 1800

1754

1758

–8

1700 1650 1600 Wavenumber (cm–1)

1550

1612 Phenyl

1690

1500

1800

Amide II

1723

Amide I

1750

1700 1650 1600 1550 Wavenumber (cm–1)

1500

(b)

10

ADMPC

CDMPC

8

5

Dry film 1% Ethanol 20% Ethanol

4

0 –5

∆A × 105

∆A × 105

1573 1554

1745

–4

1701

1750

1762

0

(a)

1070

–10

1060 1080 Wavenumber (cm–1) (c)

0

–4

Dry film 1% Ethanol 20% Ethanol

–15 1100

Dry film 1% Ethanol 20% Ethanol

4

0

–10

CDMPC

1712

1612 1577

5

–5

8

1062

1040

–8 1100

1060 1080 Wavenumber (cm–1)

1040

(d)

Figure 2.17 (See color insert.)  Effect of ethanol concentration in hexanes on the VCD spectra of ADMPC and CDMPC. (Reprinted with permission from Ma, S. L. et al., 2009, Journal of Chromatography A 1216 (18): 3784–3793, Figure 7.)

2.5  Interactions of PS Sorbents with Chiral Solutes 2.5.1  Overview The enantioselectivity S of a sorbent depends critically on the sorbent–solute interactions and secondarily on the sorbent–solvent and solvent–solute interactions. For a variety of similar molecules, S varies with apparently small and subtle differences in the solute structure. Moreover, for a given chiral solute molecule, S depends on subtle differences in the sorbent molecular structure. For PS sorbents, S varied with the type of the PS backbone (amylose or cellulose) and the type of the side chain, which determined which functional groups would be available for several simultaneous stereospecific interactions with the solute functional groups.

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Table 2.4 Retention (or Capacity) Factors of Simple Solutes on ADMPC in Hexane/IPA Solvent Solute 1-Propanol Heptane Ethanol 1-Heptanol Benzene Propylbenzene Benzyl alcohol Pyridine Tetrahydrofuran Diethylamine Aniline

Potential Binding Groups

k95/5

k90/10

k0/100

OH N/A OH OH Ph Ph OH, Ph Ph, N O NH Ph, NH2

1.4 0.0 — 1.0 0.2 0.1 2.5 1.2 0.5 0.6 2.5

— 0.0 0.6 0.5 0.2 — 1.3 — — — 1.7

— 0.1 0.1 0.1 0.2 — 0.3 — — — —

Adapted from Kasat, R. B., Y. Zvinevich, et al., 2006, Journal of Physical Chemistry B 110 (29): 14114–14122, Table 4; Kasat, R. B. et al., 2010, Chirality 22 (6): 565–579, Table 1.

Kasat, Wang, et al. (2008), Kasat, Wee, et al. (2008), and Kasat et al. (2010) reported several detailed mechanistic studies of enantioselectivities for ADMPC, ASMBC, and CDMPC, with a 90/10 vol% hexane/IPA mobile phase. Results on probing two-component sorbent-solute interactions with XRD, IR, and NMR are reviewed in Section 2.5.2 (see also Figure  2.4). The results were used along with DFT simulations of side chain/solute binary interactions. Finally, MD docking simulations were used in combination with the physical data and the DFT simulations to probe qualitatively the molecular basis of the observed enantioselectivities. The results and inferences were then compared to several important literature results. It appears that there have been few comprehensive studies that combine physical interaction data with DFT/MD simulations for sorbent–solute–solvent systems. For this reason, quantitative predictions of S values supported by physical data are still lacking; this points to needs and opportunities for future research.

2.5.2  Effect of Solute and Sorbent Structure on Enantioselectivity 2.5.2.1  Results of PPA with Three Sorbents Kasat, Wang, et al. (2008) reported HPLC studies of the chiral molecule PPA (see Figure 2.1) with three sorbents. Only with ADMPC did PPA show a significant enantioselectivity (S = 2.4; see Table 2.1). Hence, the backbone (amylose or cellulose) was shown to play a major role on S, as did the side chain for the same backbone. The retention factor of ADMPC was 4.9 for –PPA, and 2.4 for +PPA. This indicated that there was probably at least one additional strong interaction with –PPA compared to +PPA. © 2012 Taylor & Francis Group, LLC

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Ph II

75

III CDMPC/–PPA CDMPC/+PPA CDMPC ASMBC/–PPA ASMBC/+PPA ASMBC ADMPC/–PPA ADMPC/+PPA ADMPC PPA

1800

1600

1400 Wavenumber (cm–1)

1200

1000

Figure 2.18  R spectra of +PPA or –PPA with ADMPC, ASMBC, and CDMPC. The amide I and II bands are different for the two enantiomers only for ADMPC. (Adapted from Kasat, R. B., N.-H. L. Wang, et al., 2008, Journal of Chromatography A 1190 (1–2): 110–119, Figure 2.)

IR results showed that –PPA and +PPA affected the amide I and II group bands differently (Figure 2.18). Hence, in the two-component systems, the H-bonding interactions were different for +PPA versus –PPA. When S was close to 1, as with PPA with ASMBC and CDMPC, the preceding IR bands for the two enantiomers were the same. Hence, stereospecific H-bonding interactions were linked to the observed enantioselectivity. Such results were found to be consistent with those inferred from polarization-modulation IR spectroscopy data (Wirz et al. 2003, 2004) and certain VCD data (Ma et al. 2008, 2009). To further understand H-bonding interactions, Kasat, Wang, et al. (2008) used the more accurate simulation method (DFT) and the less accurate large-scale method (MD). DFT calculations of the energies of interactions of –PPA with the side chain of ADMPC allowed the calculation and ranking of the relative energies of the various possible H-bonds (Figure  2.19). This approach is limited, however, since the effects of the solvents, the interaction entropy, and intrapolymer side-chain interactions were not considered. Nonetheless, one may obtain indications of possible H-bonds, and, combined with the IR data and simulations, one may start developing hypotheses on the key interactions. For MD-docking simulations, it was important to have experimental structural information. XRD results suggested that the polymer crystallinity increased upon solute absorption (Figure  2.20). The sorbent peaks were split into two narrower peaks (a and b) upon absorption of +PPA or –PPA. No stereospecific differences were observed. The splitting allowed making the assignments of d-spacings. The © 2012 Taylor & Francis Group, LLC

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–6.93 kcal/mol

B (NH...OH)

π

C (NH...H2N)

–5.69 kcal/mol

π

–4.66 kcal/mol

π

D (C=O...H2N)

–2.51 kcal/mol

π

Figure 2.19  DFT predictions of interactions of one ADMPC side chain interacting with + or –PPA. Four types of H-bonds are found to be possible (a–d), with the conformations and the minimal energies shown. (Adapted from Kasat, R. B., N.-H. L. Wang, et al., 2008, Journal of Chromatography A 1190 (1–2): 110–119, Figure 4.)

a-peak for ADMPC and ASMBC, having spacing of 14.6 Å, was attributed to the amylose helical pitch. The a-spacing of 16.2 Å in CDMPC was attributed to the helical pitch of cellulose. The peaks b (at 18.9, 16.9, and 21.0 Å) were assigned to the repeat distance between ordered and parallel polymer rods. Having the polymer helical pitch values allowed for obtaining more realistic molecular models (MMs) of the polymer structures for the MD simulations. If single crystal XRD studies were available, one could determine the molecular structure more accurately. Using information on the type and pitch of the helical structures, a 12 mer of ASMBC or of ADMPC (three turns or unit cells of a fourfold helix), or a 9 mer of CDMPC (three turns of a threefold helix) was chosen for MM/MD simulations. The structures were energy minimized while keeping the polymer backbone atoms fixed in space and allowing the chains to relax and interact with the amide I and II groups forming certain H-bonds. This idea of a fixed backbone structure was consistent with the NMR results of CPMAS/MAS (see Section 2.3) and allowed for faster and probably more accurate computations. The MD docking simulations allowed minimizing the energies and delineating possible chain interactions. The first step in the MD docking simulations involved inspecting the cavities available for possible interactions with the chiral molecule and checking that the molecules could fit in the cavities chosen for study. Then one chiral molecule was introduced into the cavity model, with the possible H-bonding group pointing toward © 2012 Taylor & Francis Group, LLC

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b

77

CDMPC/–PPA

a

CDMPC/+PPA *

CDMPC ASMBC/–PPA

b

a *

ASMBC ADMPC/–PPA

b

a *

3

ASMBC/+PPA

5

ADMPC/+PPA ADMPC

7 2θ (degrees)

9

11

Figure 2.20 (See color insert.)  XRD spectra of three pure PS polymer films and films containing +PPA or –PPA. (Reprinted with permission from Kasat, R. B., N.-H. L. Wang, et al., 2008, Journal of Chromatography A 1190 (1–2): 110–119, Figure 5.)

possible binding sites and the simulation slightly biased toward such interactions. Energy minimization (although not guaranteed to lead to a global minimum) allowed the structures to relax to equilibrium conformations, which were different from the initial ones. One could also test other initial configurations in the same cavity or in other cavities in which a molecule could enter and fit. The MD simulations allowed for predicting the formation of H-bonds with the sorbent and possibly breaking up of some H-bonds in the dry polymer. The polymer structures were sometimes predicted to adapt or “relax” to different structures or conformations upon insertion of the chiral solute, consistently with the XRD data. MD simulations allowed predictions of interactions of solute molecules with multiple side chains in the cavity. Such interactions could be enantioselective. By contrast, even when an enantiomer had three-point interactions with a single chain, other enantiomers could have the same interactions upon approaching the chain from the other side. Then, no enantioselectivity could be predicted. This idea was confirmed with DFT simulations. If approach from the other side is sterically disallowed, as in chiral cavities, then, in principle, interactions with a single chain could be enantioselective. Nonetheless, the enantioselective interactions predicted by the MD-docking simulations involved interactions with two or more side chains. In the CDMPC example, the cavity selected for MD docking simulations was the space between the side chains from the C2 and C3 carbons of monomer 4 and the C6 carbon of monomer 5 (Figure 2.21; Kasat, Wang, et al. 2008). These side chains were © 2012 Taylor & Francis Group, LLC

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H-bond C=O(polymer)...HO(+PPA)

π

ADMPC/–PPA

X

(a)

Y

H-bond NH(polymer)...OH(–PPA)

H-bond C=O(polymer)...H2N(–PPA)

π (b)

X Z Y

Figure 2.21 (See color insert.)  MD simulations of energy-minimized structures of one ADMPC polymer cavity with docked +PPA (a) or –PPA (b). The dotted lines indicate H-bonds or π–π interactions. (Reprinted with permission from Kasat, R. B., N.-H. L. Wang, et al., 2008, Journal of Chromatography A 1190 (1–2): 110–119, Figure 6.)

predicted to be nearly parallel to each other, with the latter chain slightly shifted compared to the two former chains. Simulations for the polymer (12 mer) alone had predicted the presence of an intramolecular bond between the NH group of the C3 carbon and the C=O group of the C2 carbon. It was thus indicated that +PPA interacted with the sorbent via one H-bond, of the C=O group of the polymer with the HO group of +PPA, and a π–π interaction. By contrast, –PPA, which had the larger retention factor, interacted with the cavity more strongly, via two H-bonds and one or more (depending on how they were defined) π–π interactions. © 2012 Taylor & Francis Group, LLC

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Thus, the two-component sorbent-solute MD simulations could account qualitatively for the observed elution order. The predicted high (–18 kcal/mol) differences in the interaction energies for this large-selectivity cavity would point to a much larger value of S for that cavity than what was observed for the whole polymer. These large quantitative differences reflected several model limitations (discussed in Section 2.5.1), solvent effects, and possibly many other interactions, stereospecific or not, which were not considered in the simulations. For accurate predictions of S, one would have to consider Monte Carlo simulations of many chiral molecules interacting with multiple interacting polymer rods. No such simulations are available. The MD simulation results for +PPA or –PPA with ASMBC (for which S = 1.0) showed that there were only two interactions of each enantiomer with the sorbent and a smaller, –2 kcal/mol, energy difference. Those for CDMPC (S = 0.8) showed two interactions and a positive energy difference of +7 kcal/mol. Hence, the qualitative elution order trends for these single-cavity, single-solute molecule simulations correlated with the observed enantioselectivities. Simulations in the presence of the specific solvent are needed to test such inferences more quantitatively. 2.5.2.2  Results on Structurally Similar Compounds with CDMPC or ADMPC An alternative study (the so-called “knockout mouse” approach) to detect the key factors affecting S for the same sorbent and mobile phase was used with a series of chiral solutes having a systematically varying molecular structure. Using CDMPC, 13 chiral solutes were tested (Kasat, Wee, et al. 2008; see Figure 2.22 and Table 2.5). The potential solute functional groups are listed in Table 2.5. Only methylephedrine (MEph) showed a substantial S value of 2.1. Ephedrine and PPA showed smaller values—1.3 and 1.2—which could make the separation difficult. The results indicated that the OH and Ph groups played a major role in enantioselectivity. Similar studies were reported for 14 chiral solutes with ADMPC (Kasat et al. 2010). For ADMPC, the PPA solute (with OH, NH2, and Ph functional groups; Figure 2.1) had S = 2.4. Knocking down one of the three strong functional groups made a big difference in S. A second molecule—“2A12D” or 2-amino-1,2, diphenyl ethanol, which had all three of the preceding functional groups—was found to have an S value of 2.1. The other 12 molecules had no significant enantioselectivity, with S values ranging from 0.9 to 1.2. The most retained enantiomer in both pairs of PPA and 2A12D had a large k value (5.1 or 7.0), indicating strong interactions and pointing to two simultaneous H-bonding interactions. Similar physical characterization (IR) and molecular simulation (DFT and MD) studies as in Section 2.5.2.1 were reported for these systems and have led to hypotheses for the key interactions involved. For CDMPC with MEph, the MD simulations predicted qualitatively the observed elution order (Figure  2.23; Kasat, Wee, et al. 2008) and provided a molecular model of the key interactions. Enantioresolution was inferred to result from one H-bond, some π–π interactions, and one steric hindrance interaction. More detailed criteria for the factors affecting enantioresolution can be found in Kasat, Wee, et al. (2008). © 2012 Taylor & Francis Group, LLC

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2 Eph

CH3

HO

*

* N

3 PPA

CH3 HO

*

*

4 2A12D

CH3

CH3

H

N

HO

OH

*

*

NH2

*

CH3

CH3

* NH2

5 2A1P NH2

6 1P1P CH 3 HO

*

H

*

HO

7 APE NH 2 HO

*

8 PG OH H

H2N

OH

*

H

*

H2N

CH3

CH3

H

H

10 PD

11 1P2P H

OH *

HO

9 1A2P

12 2P1P

OH *

13 1PE

OH

CH3

H3C

*

H

HO

*

CH3

CH3

H

Figure 2.22  Molecular structures of 13 chiral solutes tested for their possible interactions with CDMPC. The chiral centers are marked with *; see also Table 2.5 for full solute names, structures, and capacity factors. (Reprinted with permission from Kasat, R. B., S. Y. Wee, et al., 2008, Journal of Chromatography B—Analytical Technologies in the Biomedical and Life Sciences 875 (1): 81–92, Figure 2.)

For ADMPC (Figure 2.24; Kasat et al. 2010), for the –2A12D enantiomer, two H-bonds were predicted along with some π–π interactions. The result could account for the large k factor observed. By contrast, the +2A12D compound was predicted to form only one H-bond. 2.5.2.3  Other Literature Results Several other important results of mechanistic studies have been reported. Because of space limitations, the reader is referred to the key relevant references. Ye et al. (2007) compared the 1H one-dimensional and two-dimensional NOESY NMR spectra of ADMPC with ethanesulfonic acid in the presence of enantiomers of p-O-tertbutyltyrosine allyl ester. The broadening of the L-enantiomer 1H-NMR bands in the presence of the polymer compared to that of the D-enantiomer was attributed to the strong interactions of the L-enantiomer with the polymer. The two-dimensional NOESY cross peaks provided information on the proximities of certain sorbent and solute protons. Based on these results and MD simulations, the authors concluded that there were stronger electrostatic and H-bonding interactions between the L-enantiomer and the ADMPC because this solute could © 2012 Taylor & Francis Group, LLC

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Table 2.5 Retention Factors and Enantioselectivities of Chiral Solutes with CDMPC (Figure 2.22) No.  1  2  3  4  5  6  7  8  9 10 11 12 13

Chiral Solute Full Name 2-Dimethylamino-1-phenylpropanol (methyl ephedrine or MEph) 2-Methylamino-1-phenyl-1-propanol (ephedrine or Eph) 2-Amino-1-phenyl-1-propanol (phenylpropanolamine, norephedrine, or PPA) 2-Amino-1,2-diphenylethanol (2A12D) 2-Amino-1-propanol (2A1P) 1-Phenyl-1-propanol (1P1P) 2-Amino-1-phenylethanol (APE) 2-Amino-2-phenylethanol (a-phenylglycinol or PG) (dl) 1-Amino-2-propanol (1A2P) (dl) 1,2-Propanediol (PD) (dl) 1-Phenyl-2-propanol (1P2P) (dl) 2-Phenyl-1-propanol (2P1P) (dl) 1-Phenylethanol (1PE)

Potential Functional Groups

k

S

OH, Ph

1.5, 0.7

2.1

OH, NH, Ph OH, NH2, Ph

1.2, 0.9 2.4, 2.0

1.3 1.2

OH, NH2, Ph, Ph OH, NH2 OH, Ph OH, NH2, Ph OH, NH2, Ph OH, NH2 OH, OH OH, Ph OH, Ph OH, Ph

3.1, 3.1 1.3, 1.3 0.9, 0.9 3.2, 3.0 2.6, 2.4 1.4, 1.4 0.9, 0.9 0.9, 0.7 0.9, 0.9 1.2, 1.0

1.0 1.0 1.0 1.1 1.1 1.0 1.0 1.3 1.0 1.2

Adapted from Kasat, R. B., S. Y. Wee, et al., 2008, Journal of Chromatography B—Analytical Technologies in the Biomedical and Life Sciences 875 (1): 81–92, Table 1. Notes: Mobile phase is n-hexane/2-propanol 90/10 v/v at 298K. The potential binding groups are listed.

fold and fit better into the polymer cavity. The authors suggested that the change in the elution order was due to the acid deprotonation, which eliminated the electrostatic interactions for both enantiomers. Upon deprotonation, the van der Waals interactions changed little for the L-enantiomer, but they increased for the D-enantiomer. Using 13C CPMAS NMR, Helmy and Wang (2005) discovered that the volume fraction of the alcohol (ethanol or IPA) in a hexane-rich mobile phase altered the ADMPC sorbent structure. These changes correlated with substantial changes in the enantioselectivity for some, but not all, enantiomer pairs tested. For these systems, MD simulations and the use of physical methods provided further insights for explaining the observed links of the solute structure to S, as discussed in Section 2.5.2.2. Bereznitski et al. (2002) studied the separation of a complex chiral solute with ADMPC. They determined the variation of S with temperature from 5°C to 70°C. Molecular simulations of the interaction energies predicted the elution order well. The enantioselectivity was attributed to differences in H-bonding interactions between the solute functional groups and the C=O groups of the sorbent. This is not surprising since such interactions can be quite strong. Ma et al. (2008, 2009) studied the enantioresolution of two aromatic a-substituted alanine esters with ADMPC and CDMPC from VCD and IR spectroscopy  data. © 2012 Taylor & Francis Group, LLC

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T

h

h X

Y Z

CDMPC/(+)–1 H-bond NH(C3)...HO((+)–1)

C6 C2

d-π

d-π X

Y Z

Figure 2.23 (See color insert.)  Predictions of MD simulations of CDMPC cavities interacting with docked MEph enantiomers (–) or (+). The dotted lines indicate H-bonds; the symbols d-π, T, and h denote π–π interactions, parallel-displaced, T-shaped, and herringbone, respectively. (Reprinted with permission from Kasat, R. B., S. Y. Wee, et al., 2008, Journal of Chromatography B—Analytical Technologies in the Biomedical and Life Sciences 875 (1): 81–92, Figure 6.)

They observed a strong dependence on S on the sorbent–solute interactions. A reversal in the elution order was observed for one compound with ADMPC, but not with CDMPC. The results underscored the importance of the polymer backbone on the cavity nanostructure and enantioselectivity (see Section 2.5.2.1). The authors concluded that the H-bonding and π–π interactions became more important with increasing ethanol concentration in the mobile phase. © 2012 Taylor & Francis Group, LLC

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2A12D

OH *

* NH2

ADMPC/(+)–14

H-bond C=O(C3)...HO((+)–14)

T

h

Z Y

(a) ADMPC/(–)–14

H-bond NH(C6)...HO((–)–14)

h

H-bond C=O(C3)...H2N((–)–14)

h Z

(b)

Y

Figure 2.24 (See color insert.)  Predictions of MD simulations of ADMPC interacting with enantiomers of 2A12D (structure shown on top); see also Figure 2.23. (Reprinted with permission from Kasat, R. B. et al., 2010, Chirality 22 (6): 565–579, Figure 5.)

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Wirz et al. (2003) studied the interactions of ASMBC with ethyl lactate enantiomers, using ACMIS (see Section 2.2.2). Stereoselective H-bonding interactions were clearly detected. The ester group of the d-enantiomer was found to interact more strongly with the NH group of the sorbent. The authors used DFT for a single side chain to elucidate the interactions. They inferred that the C=O sorbent group was also involved in the chiral recognition and that it may undergo a conformational change. No MD docking simulations were reported. In a detailed and comprehensive MD docking simulations study, Ye et al (2007) generated predictions of spatial pair distribution functions, which agreed with NMR 2D NOESY results. The enantiomers were predicted to perturb the polymer conformation differently. The L-enantiomer was predicted to fold upon interacting with ADMPC, and the D-enantiomer was predicted not to fold. The folded L-enantiomer showed stronger interactions with the sorbent.

2.5.3  Summary of Mechanisms and Methods A variety of studies has shown that the PS-based polymeric sorbents, such as the ones reviewed here, can have substantial enantioselectivities for various chiral solutes. Subtle differences in the solute or sorbent molecular structures can have a substantial impact on the enantioselectivity. Since many solutes have polar or potential hydrogen-bonding functional groups (e.g., C=O, OH, NH), these groups tend to interact significantly with sorbent functional groups, which can form H-bonds (H-bond donors or H-bond acceptors). If one enantiomer can form one H-bond and the other enantiomer can form another H-bond because of steric factors in the sorbent microstructure or cavity, then there is a basis for a strong enantioselective interaction with a strong energy difference. The solutes may contain additional functional groups (phenyl, methyl, etc.) interacting with the sorbent via weaker interaction, hydrophobic or π–π. The combination of such interactions can lead to strong selective binding sites. Such binding sites may match the three-dimensional geometry of one enantiomer, but not of the other, for steric reasons related to the cavity size or site size and the overall molecular geometry, which may be different for the polymer in the presence of the solvent and the solute compared to that for the dry polymer. It is well established that solvents, especially those containing alcohols or amines, can change the polymer structure, often by changing the state of the intrapolymer or interpolymer H-bonding. It appears that a minimum of three points (or functional groups) in the sorbent structure are needed for stereoselective interactions. It is important to establish and substantiate such interactions with a combination of direct probing experimental methods, mostly spectroscopic or calorimetric, and with molecular simulations. It is best, in principle, to obtain such information at the actual conditions of the chromatographic experiments, for the solid sorbent in the presence of the solvent. Some experiments and simulations here been done for sorbent–solute systems only, without the solvent. These results are useful, to a first approximation, even though they do not account for potentially important sorbent– solvent interactions or for solvent–solute interactions. © 2012 Taylor & Francis Group, LLC

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The most important methods that have been used for probing enantioselective interactions are IR and VCD vibrational spectroscopies, solid-state NMR (MAS and CPMAS), and calorimetric methods. The latter methods can help measure enthalpic and entropic differences of stereoselective interactions. Such differences cannot be predicted accurately from molecular simulations unless such simulations can cover all possible interactions, ranging from the most to the least enantioselective.

2.6  Conclusions and Outlook The mechanisms for molecular recognition and enantioselectivity of amylose-based and cellulose-based polymeric sorbents have been studied with various experimental methods and molecular simulations. After understanding the molecular structures of the dry polymers and the possible sites available for stereoselective interactions, several studies have focused on changes in the structures caused by the mobile-phase solvents, especially those containing hydrogen-bonding compounds such as alcohols and acetonitrile. Using the original or the solvent-modified nanostructures as a basis, various spectroscopic and molecular simulation studies have aimed at discovering sorbent adsorption sites with substantial differences in their interactions with one or a series of chiral molecules. The three-point, or three-functional, group interaction model has been found to be consistent with such studies. In this model, one enantiomer has stronger interactions with the sorbent in a least one functional group. H-bonding and phenyl–phenyl (π–π) are the most commonly involved interactions. Future studies may involve the use of more elaborate IR, VCD, and NMR methods, which may focus on probing not only the sorbent but also the chiral solute and the mobile phase. Molecular dynamics simulation studies may become more realistic, involving sorbent, solvent, and solute. Such simulations may cover several solute molecules interacting with multiple sorbent adsorption sites, such as those that would occur in a typical chromatography experiment. The practical goals are to make and test realistic and accurate predictions of the magnitude of the enantioselectivity. These predictions may allow selection of sorbent materials and solvents from the solute molecular structure or molecular predictor parameters of the molecular structure. They may also lead to concrete ideas about synthesizing more efficient sorbents.

Acknowledgments This work was supported in part by an NSF grant (CBET #0854247). We are grateful to Chiral Technologies (West Chester, PA) for helpful advice and for supplying many of the materials used in our studies. We acknowledge valuable contributions to some of our research discussed here by Professors Kendall T. Thomson, and Hugh W. Hillhouse, and by Dr. Chim Y. Chin and Yury Zvinevich, all from Purdue University. © 2012 Taylor & Francis Group, LLC

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List of Acronyms and Some Symbols A: ACMIS: ADMPC or AD: ASMBC or AS: ATR: CD: CDMPC or OD: COSY: CPMAS: CSP: DFT: DMAc: FDA: H-bonding: IR: k: LH: MAS: MD: MEph: MM: MW: NMR: NOESY: OD: PPA: PS: QSERR: RH: S: SMB: THF: VCD: XRD:

IR absorbance absolute configuration modulation infrared spectroscopy amylose tris(3,5-dimethylphenylcarbamate) amylose tris((S)-a-methylbenzylcarbamate) attenuated total reflection circular dichroism cellulose tris(3,5-dimethylphenylcarbamate) homonuclear correlation spectroscopy cross polarization magic angle spinning chiral stationary phase density functional theory dimethyl acetamide US Food and Drug Administration hydrogen bonding infrared spectroscopy retention factor, sometimes called capacity factor left handed magic angle spinning molecular dynamics methyl ephedrine molecular mechanics molecular weight nuclear magnetic resonance nuclear Overhauser enhancement spectroscopy see CDMPC norephedrine polysaccharide quantitative structure-enantioselective retention relationships right handed enantioselectivity simulated moving bed tetrahydrofuran vibrational circular dichroism x-ray diffraction

References



1. Aboul-Enein, H. Y., and I. Ali. 2001. Studies on the effect of alcohols on the chiral discrimination mechanisms of amylose stationary phase on the enantioseparation of nebivolol by HPLC. Journal of Biochemical and Biophysical Methods 48 (2): 175–188. 2. Agranat, I., and H. Caner. 1999. Intellectual property and chirality of drugs. Drug Discovery Today 4: 313–321. 3. Agranat, I., H. Caner, and A. Caldwell. 2002. Putting chirality to work: The strategy of chiral switches. Nature Reviews Drug Discovery 1: 753–768.

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4. Bellamy, L. J. 1975. The Infrared Spectra of Complex Molecules. New York: John Wiley & Sons. 5. Bereznitski, Y., R. LoBrutto, N. Variankaval, R. Thompson, K. Thompson, R. Sajonz, L. S. Crocker, J. Kowal, D. Cai, M. Journet, T. Wang, J. Wyvratt, and N. Grinberg. 2002. Mechanistic aspects of chiral discrimination on an amylose tris(3,5-dimethylphenyl) carbamate. Enantiomer 7 (6): 305–315. 6. Booth, T. D., D. Wahnon, and I. W. Wainer. 1997. Is chiral recognition a three-point process? Chirality 9: 96–98. 7. Booth, T. D., and I. W. Wainer. 1996. Mechanistic investigation into the enantioselective separation of mexiletine and related compounds, chromatographed on an amylose tris(3,5-dimethylphenylcarbamate) chiral stationary phase. Journal of Chromatography A 741 (2): 205–211. 8. Broughton, D. B. 1984. Production-scale adsorptive separations of liquid mixtures by simulated moving-bed technology. Separation Science and Technology 19 (11-1): 723–736. 9. Broughton, D. B., and C. G. Gerhold. 1961. Continuous sorption process employing fixed bed of sorbent and moving inlets and outlets. US Patent 2985589. 10. Caldwell, J. 2001. Do single enantiomers have something special to offer? Human Psychopharmacology—Clinical and Experimental 16: S67–S71. 11. Colthup, N. B., L. H. Daly, and S. E. Wiberley. 1990. Introduction to Infrared and Raman Spectroscopy. Boston: Academic Press. 12. Czerwenka, C., M. Lammerhofer, N. M. Maier, K. Rissanen, and W. Lindner. 2002. Direct high-performance liquid chromatographic separation of peptide enantiomers: Study on chiral recognition by systematic evaluation of the influence of structural features of the chiral selectors on enantioselectivity. Analytical Chemistry 74: 5658–5666. 13. Davankov, V. A. 1997. The nature of chiral recognition: Is it a three-point interaction? Chirality 9 (2): 99–102. 14. Del Rio, A., P. Piras, and C. Roussel. 2005. Data mining and enantiophore studies on chiral stationary phases used in HPLC separation. Chirality 17: S74–S83. 15. Easson, L. H., and E. Stedman. 1933. Studies on the relationship between chemical constitution and physiological action. V. Molecular dissymmetry and physiological activity. Biochemical Journal 27: 1257–1266. 16. Feibush, B. 1998. Chiral separation of enantiomers via selector/selectand hydrogen bondings. Chirality 10 (5): 382–395. 17. Franco, P., and C. Minguillon. 2001. Techniques in preparative chiral separations. In Chiral Separation Techniques: A Practical Approach, ed. G. Subramanian. New York: Wiley-VCH. 18. Francotte, E., and A. Junkerbuchheit. 1992. Preparative chromatographic separation of enantiomers. Journal of Chromatography—Biomedical Applications 576 (1): 1–45. 19. Francotte, E. R. 2001. Enantioselective chromatography as a powerful alternative for the preparation of drug enantiomers. Journal of Chromatography A 906 (1–2): 379–397. 20. Francotte, E. R., and P. Richert. 1997. Applications of simulated moving-bed chromatography to the separation of the enantiomers of chiral drugs. Journal of Chromatography A 769 (1): 101–107. 21. Ganetsos, G., and P. E. Barker. 1993. Preparative and Production Scale Chromatography. New York: Marcel Dekker, Inc. 22. Gattuso, M. J., B. McCulloch, D. W. House, W. M. Baumann, and K. Gottschall. 1996. Simulated moving bed technology—The preparation of single enantiomer drugs. Chimica Oggi-Chemistry Today 14 (11–12): 17–20. 23. Gidley, M. J., and S. M. Bociek. 1988. C-13 CP/MAS NMR-studies of amylose inclusion complexes, cyclodextrins, and the amorphous phase of starch granules—relationships

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between glycosidic linkage conformation and solid-state C-13 chemical-shifts. Journal of the American Chemical Society 110 (12): 3820–3829. 24. Harrick, N. J. 1961. Internal Reflection Spectroscopy. New York: John Wiley & Sons. 25. Helmy, R., and Wang, T. 2005. Selectivity of amylose tris (3, 5-dimethylphenylcarbamate) chiral stationary phase as a function of its structure altered by changing concentration of ethanol or 2-propanol mobile-phase modifier. Journal of Separation Science 28(2): 189–192. 26. Huthmann, E., and M. Juza. 2002. Impact of a modification in the production process of an amylose derived stationary phase on the SMB separation of a pharmaceutical intermediate. Separation Science and Technology 37 (7): 1567–1590. 27. Ikai, T., C. Yamamoto, M. Kamigaito, and Y. Okamoto. 2007. Immobilized polysaccharide derivatives: Chiral packing materials for efficient HPLC resolution. Chemical Record 7 (2): 91–103. 28. ———. 2008. Immobilized-type chiral packing materials for HPLC based on polysaccharide derivatives. Journal of Chromatography B—Analytical Technologies in the Biomedical and Life Sciences 875 (1): 2–11. 29. Juza, M., M. Mazzotti, and M. Morbidelli. 2000. Simulated moving-bed chromatography and its application to chirotechnology. Trends in Biotechnology 18 (3): 108–118. 30. Kasat, R. B., C. Y. Chin, K. T. Thomson, E. I. Franses, and N. H. L. Wang. 2006. Interpretation of chromatographic retentions of simple solutes with an amylose-based sorbent using infrared spectroscopy and DFT modeling. Adsorption—Journal of the International Adsorption Society 12 (5-6): 405–416. 31. Kasat, R. B., E. I. Franses, and N.-H. L. Wang. 2010. Experimental and computational studies of enantioseparation of structurally similar chiral compounds on amylose tris(3,5-dimethylphenylcarbamate). Chirality 22 (6): 565–579. 32. Kasat, R. B., N.-H. L. Wang, and E. I. Franses. 2007. Effects of backbone and side chain on the molecular environments of chiral cavities in polysaccharide-based biopolymers. Biomacromolecules 8 (5): 1676–1685. 33. ———. 2008. Experimental probing and modeling of key sorbent–solute interactions of norephedrine enantiomers with polysaccharide-based chiral stationary phases. Journal of Chromatography A 1190 (1-2): 110–119. 34. Kasat, R. B., S. Y. Wee, J. M. Loh, N.-H. L. Wang, and E. I. Franses. 2008. Effect of the solute molecular structure on its enantioresolution on cellulose tris(3,5-dimethylphenylcarbamate). Journal of Chromatography B—Analytical Technologies in the Biomedical and Life Sciences 875 (1): 81–92. 35. Kasat, R. B., Y. Zvinevich, H. W. Hillhouse, K. T. Thomson, N. H. L. Wang, and E. I. Franses. 2006. Direct probing of sorbent–solvent interactions for amylose tris(3,5-dimethylphenylcarbamate) using infrared spectroscopy, x-ray diffraction, solid-state NMR, and DFT modeling. Journal of Physical Chemistry B 110 (29): 14114–14122. 36. Keiderling, T. A. 2002. Protein and peptide secondary structure and conformational determination with vibrational circular dichroism. Current Opinion in Chemical Biology 6 (5): 682–688. 37. Lammerhofer, M. 2010. Chiral recognition by enantioselective liquid chromatography: Mechanisms and modern chiral stationary phases. Journal of Chromatography A 1217 (6): 814–856. 38. Lee, K. B., C. Y. Chin, Y. Xie, G. B. Cox, and N. H. L. Wang. 2005. Standing-wave design of a simulated moving bed under a pressure limit for enantioseparation of phenylpropanolamine. Industrial & Engineering Chemistry Research 44 (9): 3249–3267. 39. Lewars, E. G. 2003. Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics. London: Kluwer Academic.

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40. Lipkowitz, K. B. 1995. Theoretical-studies of type II–V chiral stationary phases. Journal of Chromatography A 694 (1): 15–37. 41. ——— 2000. Atomistic modeling of enantioselective binding. Accounts of Chemical Research 33 (8): 555–562. 42. Lipkowitz, K. B., and B. Baker. 1990. Computational analysis of chiral recognition in Pirkle phase. Analytical Chemistry 62(7): 770–774. 43. Lipkowitz, K. B., R. Coner, and M. A. Peterson. 1997. Locating regions of maximum chiral discrimination: A computational study of enantioselection on a popular chiral stationary phase used in chromatography. Journal of the American Chemical Society 119 (46): 11269–11276. 44. Lipkowitz, K. B., R. Coner, M. A. Peterson, A. Morreale, and J. Shackelford. 1998. The principle of maximum chiral discrimination: Chiral recognition in permethyl-betacyclodextrin. Journal of Organic Chemistry 63 (3): 732–745. 45. Lipp, E. D., and L. A. Nafie. 1985. Vibrational circular-dichroism in amino acids and peptides. 10. Fourier-transform VCD and Fourier self-deconvolution of the amide-I region of poly(gamma-benzyl-l-glutamate). Biopolymers 24 (5): 799–812. 46. Luthman, K., A. V. Jensen, U. Hacksell, A. Karlsson, and C. Pettersson. 1994. Discrimination of complexes between benzyloxycarbonylglycyl-l-proline and 4-hydroxy-­ 2-dipropylaminoindan in ion-pair chromatography—A molecular mechanics study. Journal of Chromatography A 666 (1–2): 527–534. 47. Lynam, K. G., and R. W. Stringham. 2006. Chiral separations on polysaccharide stationary phases using polar organic mobile phases. Chirality 18 (1): 1–9. 48. Ma, S., S. Shen, H. Lee, M. Eriksson, X. Zeng, J. Xu, K. Fandrick, N. Yee, C. Senanayake, and N. Grinberg. 2009. Mechanistic studies on the chiral recognition of polysaccharidebased chiral stationary phases using liquid chromatography and vibrational circular dichroism. Reversal of elution order of N-substituted alpha-methyl phenylalanine esters. Journal of Chromatography A 1216 (18): 3784–3793. 49. Ma, S. L., S. Shen, H. Lee, N. Yee, C. Senanayake, L. A. Nafie, and N. Grinberg. 2008. Vibrational circular dichroism of amylose carbamate: structure and solvent-induced conformational changes. Tetrahedron–Asymmetry 19 (18): 2111–2114. 50. Ma, Z., and N. H. L. Wang. 1997. Standing wave analysis of SMB chromatography: Linear systems. Aiche Journal 43 (10): 2488–2508. 51. Maier, N. M., P. Franco, and W. Lindner. 2001. Separation of enantiomers: Needs, challenges, perspectives. Journal of Chromatography A 906 (1–2): 3–33. 52. Miller, L., C. Orihuela, R. Fronek, D. Honda, and O. Dapremont. 1999. Chromatographic resolution of the enantiomers of a pharmaceutical intermediate from the milligram to the kilogram scale. Journal of Chromatography A 849 (2): 309–317. 53. Mun, S. Y., Y. Xie, J. H. Kim, and N. H. L. Wang. 2003. Optimal design of a size-exclusion tandem simulated moving bed for insulin purification. Industrial & Engineering Chemistry Research 42 (9): 1977–1993. 54. Okamoto, Y., and T. Ikai. 2008. Chiral HPLC for efficient resolution of enantiomers. Chemical Society Reviews 37 (12): 2593–2608. 55. Pasteur, L. 1901. On the asymmetry of naturally occurring organic compounds. In The foundations of Stereo Chemistry: Memoirs by Pasteur, Van’t Hoff, Lebel and Wislicenus, ed. G. M. Richardson. New York: American Book Co. 56. Pirkle, W. H. 1997. On the minimum requirements for chiral recognition. Chirality 9 (2): 103–103. 57. Pirkle, W. H., and Y. L. Liu. 1996. On the relevance of face-to-edge p–p interactions to chiral recognition. Journal of Chromatography A 749 (1–2): 19–24. 58. Rouhi, A. M. 2004. Chiral chemistry. Chemical & Engineering News 82 (24): 47–55. 59. Satinder, A. 2000. Chiral Separations by Chromatography. Washington, DC: ACS.

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60. Schaus, J. 2000. The emergence of chiral drugs. Chemical & Engineering News 78 (43): 55–78. 61. Schefzick, S., W. Lindner, K. B. Lipkowitz, and M. Jalaie. 2000. Enantiodiscrimination by a quinine-based chiral stationary phase: A computational study. Chirality 12 (1): 7–15. 62. Schulte, M., J. N. Kinkel, R. M. Nicoud, and F. Charton. 1996. Simulated moving-bed chromatograph—An efficient technique to producing optically active compounds on an industrial scale. Chemie Ingenieur Technik 68 (6): 670. 63. Sei, T., H. Matsui, T. Shibata, and S. Abe. 1992. Effect of coating solvent on chiral recognition by cellulose triacetate. In Viscoelasticity of Biomaterials, ed. W. G. Glasser and H. Hatakeyama. Washington, DC: American Chemical Society. 64. Snyder, L. R., J. J. Kirkland, and J. L. Glajch. 1997. Practical HPLC Method Development, 2nd ed. New York: John Wiley & Sons. 65. Srinivas, N. R., R. H. Barbhaiya, and K. K. Midha. 2001. Enantiomeric drug development: Issues, considerations, and regulatory requirements. Journal of Pharmaceutical Sciences 90 (9): 1205–1215. 66. Subramanian, G. 2000. Chiral Separation Techniques—A Practical Approach. Weinheim, Germany: Wiley-VCH. 67. Tachibana, K., and A. Ohnishi. 2001. Reversed-phase liquid chromatographic separation of enantiomers on polysaccharide type chiral stationary phases. Journal of Chromatography A 906 (1–2): 127–154. 68. Thomas, E. B., and P. W. S. Raymond. 1998. Chiral Chromatography. Chichester, England: John Wiley & Sons. 69. VanderHart, D. L., J. A. Hyatt, R. H. Atalla, and V. C. Tirumalai. 1996. Solid-state C-13 NMR and Raman studies of cellulose triacetate: Oligomers, polymorphism, and inferences about chain polarity. Macromolecules 29 (2): 730–739. 70. Vogt, U., and P. Zugenmaier. 1983. Investigations on the lyotropic mesophase system cellulose tricarbanilate ethyl methyl ketone. Makromolekulare Chemie-Rapid Communications 4 (12): 759–765. 71. ———. 1985. Structural models for some liquid-crystalline cellulose derivatives. Berichte Der Bunsen-Gesellschaft-Physical Chemistry Chemical Physics 89 (11): 1217–1224. 72. Wainer, I. W. 1987. Proposal for the classification of high-performance liquid-chromatographic chiral stationary phases—How to choose the right column. Trac-Trends in Analytical Chemistry 6 (5): 125–134. 73. ———. 2001. The therapeutic promise of single enantiomers: Introduction. Human Psychopharmacology—Clinical and Experimental 16: S73–S77. 74. Wang, T., and Y. D. W. Chen. 1999. Application and comparison of derivatized cellulose and amylose chiral stationary phases for the separation of enantiomers of pharmaceutical compounds by high-performance liquid chromatography. Journal of Chromatography A 855 (2): 411–421. 75. Wang, T., and R. M. Wenslow. 2003. Effects of alcohol mobile-phase modifiers on the structure and chiral selectivity of amylose tris(3,5-dimethylphenylcarbamate) chiral stationary phase. Journal of Chromatography A 1015 (1–2): 99–110. 76. Ward, T. J., and K. D. Ward. 2010. Chiral separations: Fundamental review 2010. Analytical Chemistry 82 (12): 4712–4722. 77. Wenslow, R. M., and T. Wang. 2001. Solid-state NMR characterization of amylose tris(3,5-dimethylphenylcarbamate) chiral stationary-phase structure as a function of mobile-phase composition. Analytical Chemistry 73 (17): 4190–4195. 78. Wirz, R., T. Burgi, and A. Baiker. 2003. Probing enantiospecific interactions at chiral solid–liquid interfaces by absolute configuration modulation infrared spectroscopy. Langmuir 19 (3): 785–792. © 2012 Taylor & Francis Group, LLC

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79. Wirz, R., T. Burgi, W. Lindner, and A. Baiker. 2004. Absolute configuration modulation attenuated total reflection IR spectroscopy: An in situ method for probing chiral recognition in liquid chromatography. Analytical Chemistry 76 (18): 5319–5330. 80. Xie, Y., Y.-M. Koo, and N.-H. L. Wang. 2001. Preparative chromatographic separation: Simulated moving bed and modified chromatography methods. Biotechnology & Bioprocessing Engineering 6: 363–375. 81. Xie, Y., D. J. Wu, Z. D. Ma, and N. H. L. Wang. 2000. Extended standing wave design method for simulated moving bed chromatography: Linear systems. Industrial & Engineering Chemistry Research 39 (6): 1993–2005. 82. Yamamoto, C., and Y. Okamoto. 2004. Optically active polymers for chiral separation. Bulletin of the Chemical Society of Japan 77 (2): 227–257. 83. Yamamoto, C., E. Yashima, and Y. Okamoto. 1999. Computational studies on chiral discrimination mechanism of phenylcarbamate derivatives of cellulose. Bulletin of the Chemical Society of Japan 72 (8): 1815–1825. 84. ———. 2002. Structural analysis of amylose tris(3,5-dimethylphenylcarbamate) by NMR relevant to its chiral recognition mechanism in HPLC. Journal of the American Chemical Society 124 (42): 12583–12589. 85. Yashima, E., H. Fukaya, and Y. Okamoto. 1994. 3,5-Dimethylphenylcarbamates of cellulose and amylose regioselectively bonded to silica-gel as chiral stationary phases for high-performance liquid-chromatography. Journal of Chromatography A 677 (1): 11–19. 86. Yashima, E., C. Yamamoto, and Y. Okamoto. 1996. NMR studies of chiral discrimination relevant to the liquid chromatographic enantioseparation by a cellulose phenylcarbamate derivative. Journal of the American Chemical Society 118 (17): 4036–4048. 87. Ye, Y. K., S. Bai, S. Vyas, and M. J. Wirth. 2007. NMR and computational studies of chiral discrimination by amylose tris(3,5-dimethylphenylcarbamate). Journal of Physical Chemistry B 111 (5): 1189–1198. 88. Zugenmaier, P., and H. Steinmeier. 1986. Conformation of some amylose triesters—The influence of side groups. Polymer 27 (10): 1601–1608.

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Chromatographic Separation and NMR An Integrated Approach in Pharmaceutical Development Nina C. Gonnella

Contents 3.1 Introduction.....................................................................................................94 3.2 NMR Theory...................................................................................................94 3.2.1 Magnetic Properties of Nuclei.............................................................94 3.2.2 Nuclear Resonance and Relaxation..................................................... 96 3.2.3 The Chemical Shift.............................................................................. 98 3.2.4 Spin Coupling......................................................................................99 3.3 LC-NMR Instrumentation and Method Development.................................. 100 3.4 Probe Technologies........................................................................................ 103 3.4.1 Room Temperature Flow Probe......................................................... 103 3.4.2 Room Temperature Microcapillary Flow Probe............................... 104 3.4.3 Cryogenically Cooled Probes............................................................ 105 3.4.3.1 Cryoflow Probe................................................................... 105 3.4.3.2 Cryocapillary Probe............................................................ 106 3.5  NMR Associated Isolation Technologies....................................................... 106 3.5.1 Stop Flow........................................................................................... 107 3.5.2 Loop Collector................................................................................... 108 3.5.3 Solid Phase Extraction....................................................................... 109 3.5.4 Capillary Electrophoresis–NMR....................................................... 112 3.6 NMR Experiments......................................................................................... 113 3.7 Applications................................................................................................... 115 3.7.1 Degradation Products........................................................................ 115 3.7.2 Impurities........................................................................................... 117 3.7.3 Trace Analysis................................................................................... 119 3.7.4 Analysis of Mixtures......................................................................... 122 3.7.5 Tautomer Kinetics.............................................................................. 123 3.7.6 Unstable Products.............................................................................. 125

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3.7.7 Metabolites........................................................................................ 127 3.7.8 CE Isolates......................................................................................... 129 3.8 Summary....................................................................................................... 130 References............................................................................................................... 132

3.1  Introduction Nuclear magnetic resonance (NMR) is a powerful technology that has been extensively used for the structural elucidation and characterization of organic, inorganic, and biological molecules. Sophisticated advances in spectroscopic instrumentation along with advances in multidimensional NMR and solvent suppression techniques have vastly expanded the range and breadth of NMR capabilities. This has been realized particularly with respect to the more challenging issues regarding sensitivity and limits of detection. These advances have had an acute impact on the hyphenated chromatographic-NMR capabilities. The coupling of separation systems, such as high performance liquid chromatography (HPLC), with NMR spectroscopy has been at the forefront of emerging and cutting-edge technologies. From its initial introduction in 1978 [1], LC-NMR has matured into a viable analytical tool for structure identification and characterization [2]. Combined improvements in magnet design, probe technology, solvent suppression techniques [3], and automation have contributed to its scope and utility in the pharmaceutical industry. The advances in automation and sensitivity have pushed the limits of detection to enable unprecedented mass sensitivity for NMR detection. In addition, numerous modes of isolation have been developed and integrated with the NMR technology in an automated fashion to facilitate the process. Some of these include continuous flow detection, stop flow, solid phase extraction (SPE), loop collection, and capillary electrophoresis [2–4]. Overall, LC-NMR has evolved into a robust technology that is now considered to be nearly routine [5]. Numerous reviews on chromatographic-NMR hyphenated systems have been written, some of which can provide a more detailed description of the technology with an historical perspective [2,4–9]. This review will provide an introduction to NMR theory and an update on recent advances in system performance and will focus on current developments in chromatographic NMR integration, with particular emphasis on applications and utility in pharmaceutical development.

3.2  NMR Theory 3.2.1  Magnetic Properties of Nuclei Nuclear magnetic resonance is a phenomenon that exists when certain nuclei are placed in a magnetic field and are subsequently perturbed by an orthogonal oscillating magnetic field. This phenomenon occurs for nuclei that possess a property called spin. This property induces a spinning charge that creates a magnetic moment μ. The magnetic moment μ of a nucleus is proportional to its spin, I, its © 2012 Taylor & Francis Group, LLC

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magnetogyric ratio, γ (a property intrinsic to each nucleus), and Planck’s constant, h: µ=



γlh 2π

(3.1)

Because of their magnetic properties, these nuclei may be likened to tiny bar magnets. When such nuclei are placed in a magnetic field, some will align with the field and others against the field. Those nuclei aligned with the field are at a lower energy level than those aligned against the field. The separation in energy levels is proportional to the external magnetic field strength. The energy of a nucleus at a particular energy level is given by E=−



γh mB 2π

(3.2)

where B is the strength of the magnetic field at the nucleus and m is the magnetic quantum number. The difference in energy between the transition energy levels is ΔE = −



γhB 2π

(3.3)

Hence, as the magnetic field, B, is increased, so is ΔE (Figure 3.1). Also, if a nucleus has a relatively large magnetogyric ratio, then ΔE will be correspondingly large. Because the separation in energy levels (ΔE) affects the Boltzmann distribution of the populated energy states, higher magnetic fields and larger magnetogyric properties of nuclei will increase the population of the lower energy state and hence

β E

1

H high energy spin state

υ = 500 MHz υ = 600 MHz

α 0 Tesla

1H

low energy spin state

11.7 Tesla 14.1 Tesla Bo

Figure 3.1  Graphical relationship between magnetic field (Bo) and frequency for 1H NMR energy absorptions. © 2012 Taylor & Francis Group, LLC

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the number of possible NMR transitions will increase. These properties will correspondingly enhance the sensitivity of the NMR experiment [10]. As noted previously, only certain atoms possess a magnetic moment because, for many atoms, the nuclear spins are paired against each other such that the nucleus of the atom has no overall spin. However, for atoms where the nucleus does possess unpaired spins, such atoms can experience NMR transitions. The rules for determining the net spin of a nucleus are as follows: • If the number of neutrons and the number of protons are both even, then the nucleus has no spin. • If the number of neutrons plus the number of protons is odd, then the nucleus has a half-integer spin (i.e., 1/2, 3/2, 5/2). • If the number of neutrons and the number of protons are both odd, then the nucleus has an integer spin (i.e., 1, 2, 3). Nuclei most often observed in pharmaceutical applications are shown in Table 3.1.

3.2.2  Nuclear Resonance and Relaxation Nuclei can be imagined as spheres spinning on their axes. The phenomenon of nuclear resonance can be illustrated using a quantum mechanical description. Quantum mechanics shows that a nucleus of spin I will have 2I + 1 possible orientations. For a nucleus with spin 1/2, two possible orientations exist, occupying discrete energy levels in the presence of an external magnetic field (Figure 3.2). Each level is given a magnetic quantum number, m. The initial populations of the energy levels are determined by thermodynamics, as described by the Boltzmann distribution. The lower energy level will contain slightly more nuclei than the higher level. It is possible to excite these excess nuclei into the higher level with a band of radio frequency waves (Figure  3.3). The frequency of radiation needed for an energy transition to occur is determined by the difference in energy between the energy levels. Table 3.1 Properties of Commonly Observed Nuclei in NMR Spectroscopy H 13C 15N 17O 19F 27Al 29Si 31P 11B 1

I

Y107 T–1 s–1

1/2 1/2 1/2 5/2 1/2 5/2 1/2 1/2 3/2

26.752 6.728 –2.713 –3.628 25.182 6.976 –5.319 10.839 8.584

ν/MHz (at 14.1 T) 600.00 150.85 60.81 81.33 564.51 156.32 119.19 242.86 192.48

Natural Abundance 99.99% 1.1% 0.37% 0.04% 100% 100% 4.7% 100% 80.1%

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Energy

Applied magnetic field

0

m = –1/2

No field

m = +1/2

Figure 3.2  Zeeman interaction: In the absence of a magnetic field, magnetic dipoles are randomly oriented and there is no net magnetization. Upon application of a magnetic field, nuclei occupy discrete energy levels. Two energy levels exist for nuclei with spin quantum number of 1/2. Two spin states for I = 1/2 m1 = –1/2 or β

–1/2

m1 = +1/2 or α

+1/2

∆E = |γ(h/2π)B|

Figure 3.3  Illustration of spin states for nuclei aligned with α or against β for the external magnetic field (Bo). Transitions between these spin states can occur by applying a radio frequency field B1.

A classical mechanical description has also been used to describe the resonance phenomenon. This description invokes the use of vectors to illustrate the magnitude and direction of the magnetic properties of the nucleus (Figure  3.4). When placed in a magnetic field, a nucleus with spin will tend to precess about the direction of the field at a discrete frequency. This frequency is known as the Larmor precessional frequency. For a magnet of 11.75 T, a proton will precess at 500 MHz and, for 14.1 T, a proton precesses at 600 MHz. NMR spectrometers are commonly named based upon the Larmor precessional frequency of protons at a particular field strength. Bo

Figure 3.4  Classical mechanical illustration of a nucleus (of spin 1/2) in an applied magnetic field (Bo). When the nucleus is in a lower energy state, it is aligned with the field. The nucleus may be viewed as a sphere spinning on its axis. In the presence of a magnetic field, the axis of rotation will precess around the direction of Bo. © 2012 Taylor & Francis Group, LLC

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If a sample is placed in an 11.75 T magnet and a radio frequency field is applied at 500 MHz, the protons will absorb that energy and the phenomenon known as resonance occurs. Hence, for nuclei of spin 1/2 in a magnetic field, the nuclei in the lower energy level will be aligned in the direction of the field and the nuclei in the higher energy level will align against the field. Because the nucleus is spinning on its axis, in the presence of a magnetic field, this axis of rotation will precess around the direction of the external magnetic field. The frequency of precession, the Larmor frequency, is identical to the transition frequency. The potential energy of the precessing nucleus is given by

E = –μB cos θ

(3.4)

where θ is the angle between the direction of the applied field and the axis of nuclear rotation. When energy is absorbed by the nucleus, the angle of precession, θ, will change. For a nucleus of spin 1/2, absorption of radiation “flips” the magnetic moment so that it opposes the applied field (the higher energy state). Since only a small excess of nuclei exist in the lower energy state to absorb radiation, only a small number of transitions can occur. The low numbers of energy transitions are what give rise to the observed NMR signal; hence, this condition negatively affects the overall sensitivity of the technology. By exciting the low-energy nuclei, the populations of the higher and lower energy levels will become equal, resulting in no further absorption of radiation. The nuclear spins are then considered saturated. When the radio frequency pulse is turned off, the nuclei undergo a relaxation process, returning to thermodynamic equilibrium [11]. In NMR spectroscopy, two primary relaxation processes occur. They are termed spin–lattice (longitudinal) relaxation (T1) and spin–spin (transverse) relaxation (T2). Spin–lattice relaxation T1 is the time it takes an excited nucleus to release its energy to its lattice or surrounding environment. It is dependent on the magnetogyric ratio of the nucleus and the mobility of the lattice. Spin–spin relaxation T2 describes the interaction between neighboring nuclei causing inhomogeneity in the local magnetic field on a microscopic scale. This relaxation phenomenon can result in line broadening of the NMR signal. Both these relaxation processes need to be taken into account in the design and execution of NMR experiments [11].

3.2.3  The Chemical Shift All nuclei in a molecule do not experience the same local magnetic field because the magnetic field at the nucleus is not equal to the applied magnetic field. Electrons around the nucleus create an opposing magnetic field that shields a nucleus from the applied field (Figure 3.5). The difference between the applied magnetic field and the field at the nucleus is called nuclear shielding. Nuclear shielding leads to the property known as chemical shift, which is a function of the nucleus and its environment. It is measured relative to a reference compound causing the calculated value to be independent of the external magnetic field strength. For 1H NMR, the reference is usually tetramethylsilane, Si(CH3)4. This reference was selected because it is inert, nonreactive, and stable. In addition, its resonance falls © 2012 Taylor & Francis Group, LLC

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Bo e

Figure 3.5  The electrons around a nucleus (e.g., a proton) create a magnetic field that opposes the applied field. This reduces the field experienced at the nucleus; hence, the electrons provide local shielding effect.

outside the region of the resonances for most molecules of interest and its volatility enables it to be removed easily from the sample. The equation for calculating the chemical shift is



Chemical shift, δ =

Frequency of signal − frequency of reference × 10 6 (3.5) spectrometer frequency

Because the chemical shift is dependent upon the environment surrounding each nucleus, it provides a wealth of information that may be used in defining and characterizing a chemical structure [10,11].

3.2.4  Spin Coupling Spin–spin coupling is another property that plays a critical role in structure elucidation. For proton–proton interactions, when signals for single protons appear as multiple lines, this is due to 1H–1H coupling (spin–spin splitting or J-coupling). The spin–spin splitting arises as a result of internuclear magnetic influences. As mentioned previously, protons may be viewed as tiny magnets that can be oriented with or against the external magnetic field. For a molecule containing a proton (HA) attached to a carbon that is attached to another carbon containing a proton (HB), HA feels the presence of the magnetic field of HB. When the field created by HB reinforces the magnetic field of the NMR instrument (B0), HA experiences a slightly stronger field, but when the field created by HB opposes B0, HA experiences a slightly weaker field. The same situation occurs for HB relative to magnetic influences from HA. The result is two signals for HA and two signals for HB, commonly termed a doublet. The magnitude of the observed spin splitting depends on many factors and is given by the coupling constant J (units of hertz). J is the same for both partners in a spin-splitting interaction and is independent of the external magnetic field strength. Equivalent nuclei do not interact with each other. For example, the three methyl protons in ethanol cause splitting of the neighboring methylene protons; they do not cause splitting among themselves. © 2012 Taylor & Francis Group, LLC

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1

4

Doublet one coupled hydrogen

1 2

3

1

Singlet no coupled hydrogens

4

H H

H

H H H Quartet three coupled hydrogens H

1

3 6

Triplet two coupled hydrogens

1

H

H

1

Figure 3.6  The splitting pattern of a given nucleus (or set of equivalent nuclei) with spin 1/2 can be predicted by the n + 1 rule, where n is the number of neighboring spin-coupled nuclei with the same or similar coupling constants. The intensity ratio of these resonance lines follow Pascal’s triangle. A doublet has equal intensities, a triplet has an intensity ratio of 1:2:1, a quartet 1:3:3:1.

For nuclei with the quantum spin number of 1/2, the multiplicity of a resonance is given by the number of equivalent protons in neighboring atoms plus one (i.e., the n + 1 rule). The coupling pattern follows Pascal’s triangle, shown in Figure 3.6. For organic molecules, the nuclei commonly studied by NMR spectroscopy are proton and carbon-13. These nuclei, along with sophisticated experiments that include indirect detection and solvent suppression techniques, are critical for most organic structure elucidation. This is particularly true for hyphenated technologies such as LC-NMR, where indirect methods are required for detection of low natural abundance nuclei such as 13C and where suppression of mobile phase solvents is required for analyte signal detection. Such experiments are covered in Section 3.6. To enable and enhance the performance of LC-NMR and related studies, significant advances in NMR instrumentation, method development, and probe technology were necessary. Many improvements in instrument sensitivity, range of capability, component integration, and automation design have resulted in significant breakthroughs in the limits of detection for structural characterization.

3.3  LC-NMR Instrumentation and Method Development LC-NMR integrates the separation capabilities of HPLC with the structure elucidation capabilities of NMR to produce a hyphenated analytical instrument. With this system, a sample mixture may be separated into individual components by injection into the HPLC unit. The separated fractions are then transferred to a flow probe in the NMR spectrometer. Because compound identification and structural elucidation using NMR is nondestructive, the compounds can be easily recovered. Both the HPLC and NMR systems can be operated independently. © 2012 Taylor & Francis Group, LLC

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The LC-NMR system comprises an NMR spectrometer console, a superconducting magnet, a workstation, and a flow probe—all under the operation of specialized LC-NMR software. The HPLC portion is composed of an HPLC pump, HPLC column(s), variable-wavelength UV detector and/or photo diode array detector, and an LC workstation that may be set up for stop flow or continuous flow. Timing for movement of a peak between the different positions in the hyphenated system must be carefully calibrated. The time required for a peak to reach the NMR probe or a designated collection unit depends upon the void volume between the LC unit and the collection unit or probe flow cell. This will depend upon flow rate. In order to allow selection of desired peaks, the separation is monitored by an LC detector, usually a UV detector that displays a chromatogram of the separation. The chromatography software allows certain positions in the chromatogram to be manually or automatically selected for further measurement. The NMR probe or storage compartment is located downstream of the UV detector and is estimated to be reached about 10–40 s after the first peak appears in the LC detector [5]. The software calculates the appropriate delays to capture the peak at its desired position where the necessary actions for storage or measurement are initiated. Software is commercially available from instrument vendors that allows interactive selection of the peaks from the chromatogram and automatic calculation of the time delays. A typical LC-NMR system configuration is shown schematically in Figure 3.7. Analytical chromatographic separation of small organic molecules is usually carried out using reversed phase chromatography. When considering column selection, silica-based C18 or C8 columns are usually chosen because of their high efficiency and stability. Factors such as flow rate, temperature, and gradient composition will affect separation of the analyte mixture and need to be adjusted to obtain optimal conditions. The appropriate method for good analyte separation may be developed independently of the LC-NMR system and transferred at a later time. The basic conditions of a chromatographic separation conducted for an LC-NMR experiment are the same as those required for ordinary analytical chromatography. However, the transfer of chromatographic methods to the LC-NMR system requires buffer and solvent considerations. Buffer selection can be an important consideration since highly protonated buffers such as ammonium acetate will produce large proton signals that can affect the receiver gain settings and create dynamic range issues that will interfere with observation of the low-level analytes of interest. This is further compounded by the large signals from the mobile phase solvents H2O and acetonitrile or methanol. Although the proteosolvent and buffer signals can be suppressed with sophisticated pulse sequences (see Section 3.6) problems arise due to excessive overlay of the suppressed peaks with analyte peaks of interest. Phosphate buffers or trifluoroacetic acid (TFA) additives, however, are well suited for NMR evaluation since they do not contain nonexchangeable protons to complicate the spectrum. The large solvent signal problem may be partially alleviated with the use of D2O since this deuterated solvent is not cost prohibitive. However, D2O will cause deuterium exchange with the analyte eliminating observation of exchangeable protons that may be critical for © 2012 Taylor & Francis Group, LLC

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Console

HPLC pump Injector By-pass 600 Column

Sample collection module UV detector

Capillary junctions

Direct SPE loop

Waste

Electronic junctions

Figure 3.7  Illustration of a typical LC-NMR configuration. The NMR spectrometer is integrated with a liquid chromatography system. The sample may be transported directly from the column to the probe. Other common collection modules include a solid phase extraction (SPE) system or loop collector. Capillary junctions are designated with solid lines and electronic junctions with dashed lines.

structure elucidation. Hence, when developing a method for transfer to an LC-NMR system, the composition of the mobile phase must be carefully determined. Although additives such as phosphate and TFA may be ideal for NMR detection, if the method needs to be compatible with mass spectrometry (MS), such buffers can be problematic because phosphate buffers tend to crystallize out and contaminate the MS ion source. In addition, TFA is not usually compatible with electrospray ionization (ESI)-MS since it causes ion suppression as a result of strong ion pairing between the TFA anion and the protonated analyte. In negative ion mode, TFA suppresses the analyte by competing for charge. While careful control of buffer and mobile phase composition is important for successful execution of an LC-NMR experiment, this is not a factor when the system employs solid phase extraction as a means of trapping the analyte. With SPE, LC methods can be transferred to the LC-NMR system without concern for such compatibility issues (see Section 3.5.3). © 2012 Taylor & Francis Group, LLC

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3.4  Probe Technologies It is well known that NMR spectroscopy is inherently an insensitive technique. From an instrumentation standpoint, the sensitivity of NMR spectroscopy depends on three parameters: The magnetic field strength (sensitivity increases with magnetic field strength) The size and filling factor of the receiver coil (mass sensitivity increases with increasing fill factor and decreasing coil diameter) The noise introduced during detection Although sensitivity will increase with increasing magnetic field, this is not always a cost-effective solution. Magnetic field strengths are now commercially available at 900 MHz and beyond; however, these systems are expensive. Relative to a 900 MHz spectrometer, a 600 MHz spectrometer will possess half the sensitivity but can be purchased at a considerably lower cost [12]. More cost-effective efforts to further improve sensitivity have centered on improving probe performance [13,14]. Reduction of thermal noise was addressed with the development of cryogenically cooled probes. In addition, development of probe geometries with smaller receiver coils and better fill factors has had a major impact on sensitivity. These advances in probe technology are particularly attractive since probes may be easily added or retrofitted to existing spectrometers at a fraction of the cost of a higher field spectrometer. Following is a discussion of the various advancements in probe design used in supporting LC-NMR studies.

3.4.1  Room Temperature Flow Probe Flow probes for NMR spectroscopy have been designed for both manual and automated use. The properties of a flow NMR probe need to incorporate a number of criteria. When a flow probe is interfaced with an HPLC/column unit, the system must be robust enough to sustain connection and flow transfer through capillary tubing. The flow probe must possess an enhanced “filling factor” to achieve maximum sensitivity on a chromatographically isolated peak. This becomes particularly important for low-level quantities of isolates where signal to noise is challenged by minimal sample concentration. In addition, care must be taken to eliminate leaks, clogs, and air bubbles in the NMR flow cell, leading to degraded NMR line shape from magnetic-susceptibility inhomogeneities. To enable maximum flow cell performance, NMR flow probes are designed with the inlet to the probe at the bottom of the flow cell (vertically aligned with the magnetic field) and the outlet from the top of the flow cell (Figure 3.8). This configuration is conducive to the elimination of air bubbles. A variety of high-resolution flow NMR probes are commercially available and are considered to be standard items from NMR vendors. NMR flow probes are designed with optimized flow cell size for chromatographic peaks and minimized band broadening during sample transfer. These probes are built for high sample throughput. By linking the flow probe to a chromatography system, direct transfer of a sample © 2012 Taylor & Francis Group, LLC

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1.7 mm capillary

Out In Helmholtz coil Flow probe vs. capillary probe

Figure 3.8  Illustration of a flow probe and a capillary cryoprobe. Both probes may be configured with 30 mL flow cell volume. 

into the NMR probe is possible. This direct transfer has the advantage of minimizing sample handling and thus the danger of contamination and decomposition of samples. Because the probe is the only modification to the NMR spectrometer required for flow applications, a probe change can be done in minutes and preserve the versatility of the instrument. Flow probes are available on spectrometers ranging in field strength from 300 to 900 MHz. Typical flow cell sizes are 30, 60, and 120 mL, although microcapillary probes are also available (see next section). The NMR probe configurations available possess multinuclear capability including 19F. Flow probes are currently available with gradient shimming and automatic tune and match, which vastly increase the utility and ease of use of LC-NMR systems.

3.4.2  Room Temperature Microcapillary Flow Probe To enable quality NMR data to be obtained from shrinking sample sizes, capillary room temperature NMR probes (CapNMR) were developed and are commercially available. These probes have a flow cell capacity of either 5 or 10 μL. Popular probe configurations include 1H with 13C indirect detection or triple resonance inverse probes with 1H, 13C, and 15N or 31P. CapNMR probes enable hundreds of samples of isolated compounds to be run per day using 96 or 384 well microplates. The CapNMR system requires a new approach to sample preparation. Instead of preparing a sample in a conventional 5 mm glass NMR tube containing 200–600 μL of deuterated solvent, the CapNMR sample is dissolved in only 5–10 μL of solvent. The solution is then transferred into the capillary probe either manually using a syringe or by using an automated liquid-handling system. It is important to note that this techno­ logy requires scheduled cleaning protocols to ensure reproducible results. © 2012 Taylor & Francis Group, LLC

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A comparison of CapNMR flow-cell probes to that of traditional 5 mm sampletube-based probes revealed significantly higher mass sensitivity for the capillary configuration. CapNMR even improves the sensitivity of NMR spectroscopy beyond that achieved by using Shigemi-type tubes where the sample volume is reduced by half and a two- to threefold net increase in mass sensitivity is realized. Gronquist et al. directly compared spectra obtained with both CapNMR and 5 mm probe designs by using a 10 mM sucrose solution. In one series of experiments, onedimensional 1H NMR spectra as well as two-dimensional (1H, 13C) heteronuclear multiple quantum correlation spectroscopy (HMQC) and (1H, 13C) heteronuclear multiple bond correlation (HMBC) spectra were acquired for a 5 μL sample of a solution of sucrose (10 mM) injected into the CapNMR probe by syringe. In a second series of experiments, the same amount of sucrose was dissolved in the volume of solvent (D2O) required using a 5 mm Shigemi tube, followed by acquisition of an equivalent set of spectra using a conventional 5 mm H{C,N} probe and the same spectrometer. A comparison of the 1H spectra revealed that the signal-to-noise ratio was about five times better for the CapNMR spectrum over that found using the Shigemi tube [15]. In addition, the residual water peak in the CapNMR spectrum was several orders of magnitude smaller than in the spectrum obtained using a 5 mm probe since the active volume is over 100 times greater in the 5 mm sample than that of the CapNMR 5 μL flow cell. The vastly reduced water peak enables higher receiver gain, which contributes to the observed sensitivity gain. Indirect detection using carbon–proton correlation experiments HMQC, heteronuclear single quantum correlation spectroscopy (HSQC), and HMBC has also been reported using CapNMR. Because of the low natural abundance of 13C, the sensitivity of these experiments in producing sufficient signal to noise for structure determination can often be challenging. However, because CapNMR probes are equipped with gradient coils, sensitivity-enhanced gradient versions of the HMQC and HMBC experiments are possible. This leads to improved signal intensity. Also, smaller solvent signals enable appropriate receiver gain adjustment and contribute to higher sensitivity for the indirect detection experiments [12].

3.4.3  Cryogenically Cooled Probes Improving signal to noise is a major challenge in NMR spectroscopy. The conventional solutions are to increase the signal intensity by increasing field strength or sample concentration, or via signal averaging; however, another approach is to decrease the noise. This has been accomplished by cryogenically cooling the electronics in the NMR probe to reduce thermal noise. The resulting probe is called a cryoprobe, or a cold probe. Cryogenically cooled probes operate at a temperature of 25 °K and provide about a fourfold signal-to-noise improvement relative to their room-temperature counterpart [16]. These probes have been designed for a range of sample sizes that include capillary tubes up to 5 mm and flow cells [13,17,18]. 3.4.3.1  Cryoflow Probe When the electronics of the NMR probe are cooled, the signal to noise of the resulting NMR spectra will increase [19]. Initially, 5 mm probes for solution-state NMR © 2012 Taylor & Francis Group, LLC

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studies were cooled to 25 °K, resulting in a fourfold increase in sensitivity [16,20]. Later, flow accessories were added to the 5 mm cryoprobe, increasing sensitivity [17]. Because a cryogenically cooled flow probe greatly improves NMR sensitivity, it can be readily used as a high-throughput analysis tool, although care must be taken to avoid flow-cell contamination. As with all flow probes used in a high-throughput manner, cleaning and maintenance of the system need to be carried out to avoid contaminant carryover. Many developments have expanded the capability of NMR flow cells. Flow probes currently incorporate improved fluidics, temperature control, and a wide range of sample-cell sizes. When combined with cryogenic cooling, substantially better sensitivity is now available. New capillary separation techniques can be supported, and multiplex NMR that allows solution-state NMR to be truly parallel is also possible [5]. Cryogenic flow probes can also be interfaced with an SPE system and a loop collector. These developments have greatly expanded the range of LC-NMR applications. 3.4.3.2  Cryocapillary Probe Microcryotechnology is commercially available with the 1.7 mm TCI MicroCryo Probe from Bruker Biospin. This probe represents the current state of the art in mass sensitivity [21]. The sample volume is 30 μL and offers more than an order of magnitude in mass sensitivity compared to the conventional 5 mm probe. It allows for highest 1H sensitivity as well as enhanced performance for carbon. A comparative illustration of a 1.7 mm capillary tube is given in Figure 3.8. The extreme sensitivity provides a powerful tool for NMR analysis of limited sample amounts. Applications are particularly targeted toward isolated materials in low abundance. These may include degradents, process impurities, extractables, natural products, peptides or small molecules, proteins that are difficult to express, etc. This probe enables acquisition of spectra that allow difficult problems to be tackled and solved, particularly when only microgram or submicrogram quantities of material are available. Because the sensitivity gain is 14-fold over a conventional room temperature 5 mm probe, a 200-fold reduction in experiment time can be realized. The probe is optimized for direct proton detection with indirect detection for 15N and 13C. Short pulses and large bandwidths for 15N are ideal for small molecule structure elucidation. Incorporation of Z-gradients enables signal enhancement and solvent suppression. The probe covers a temperature range of 0°C–80°C. In addition, the 30 μL volume perfectly matches the elution volume of HPLC-SPE. Isolated samples from SPE may be sent directly to a 1.7 mm tube in manual mode or in automation using a fraction collector.

3.5  NMR Associated Isolation Technologies Hyphenated NMR instruments have evolved to include a number of automated operation modes. These LC-NMR modes include continuous flow, stop flow, loop collection, and solid phase extraction [4]. As noted previously, LC peaks of interest for the NMR transfer require the use of a non-NMR detector. Detection systems such as UV, diode array detector (DAD), and MS are compatible with the gradient LC © 2012 Taylor & Francis Group, LLC

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methods that are required to keep the eluting peaks as sharp as possible. For flow methods, this is critical in preserving NMR sensitivity. With continuous flow LC-NMR, the sample from the chromatographic column is guided through a flow cell into a dedicated NMR flow probe. The time for one measurement is determined by the chromatographic flow rate and is typically between 8 and 20 s. Active flow cell volumes range from 30 to 120 μL. This approach requires the use of deuterated solvents and solvent suppression techniques to mediate the dynamic range effects where the huge solvent peaks mask the peaks from the compound of interest. Continuous flow experiments work most effectively for cases where significant amounts of analyte can be isolated from a single chromatographic injection. This approach is best suited for compounds that have stability issues and cannot be stored for significant periods of time. While there are cases where continuous flow LC-NMR is preferred, this review will focus on the more robust collection modes of stop flow, loop collection, and SPE that enable full structure characterization. In addition, the emerging capillary electrophoresis (CE) isolation in conjunction with microflow detection will be explored.

3.5.1  Stop Flow Signal-to-noise limitations are a major challenge in many LC-NMR studies. Although NMR signal to noise can be improved by signal averaging, this requires the flow to be stopped with the chromatographic peak of interest in the flow cell for a substantial period of time. During this period, multiple scans of the chromatographic peak’s NMR spectrum may be carried out to achieve an acceptable signal-to-noise level. With stop-flow analysis, the chromatographically separated sample is analyzed under static conditions. A compound separated by HPLC is sent directly to the NMR flow cell and is stopped in the NMR flow probe for as long as is needed for NMR data acquisition. Stop flow requires the calibration of the time required for the sample to travel from the detector of the HPLC to the NMR flow cell. Timing depends upon the flow rate and the length of the tubing connecting the HPLC with the NMR. Because the chromatographic peak of interest is stopped in the flow cell, two-dimensional homonuclear and heteronuclear NMR correlation experiments [3] can be obtained. The time the compound resides in the flow cell is under complete control of the spectroscopist. There are several ways to acquire stopped-flow data. One approach involves stopping the chromatographic peaks of interest in the NMR flow probe as they elute from the chromatography column. Alternatively, the LC pump may be programmed to “time slice” through a chromatographic peak, stopping every few seconds to acquire a new spectrum. This can be useful for resolving multiple components by NMR from within a peak that is not fully resolved chromatographically, or for verifying the purity of a chromatographic peak. However, with such mixtures, substantial amounts of material are required to obtain interpretable spectra in a few scans. In order to use stop flow to collect NMR data on a number of chromatographic peaks in a series of stops during the chromatographic run without incurring on-column © 2012 Taylor & Francis Group, LLC

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diffusion, the NMR data for each chromatographic peak must be acquired in a short time. It is estimated that 30 min or less are required to prevent diffusion effects when more than four peaks need to be analyzed, and less than 2 h for the analysis of no more than three peaks [22,23]. The use of commercially available cryoprobes or cold probes improves the sensitivity of the stop-flow mode (see Section 3.4.3). Stop flow is preferred when the chromatography produces reasonably well separated peaks and the compound is stable in solution for extended periods of time. Other methods utilizing the stopped flow approach involve loop collection or trapping the eluted peaks onto a minichromatographic column (solid phase extraction cartridge). These methods are discussed in more detail in the following sections.

3.5.2  Loop Collector Unlike stop flow, loop collectors allow separation of the LC and NMR functions. With loop collection, the sample undergoes chromatographic separation, but instead of sending the sample directly to the NMR probe, the peaks corresponding to individual compounds are trapped and stored on capillary tubing or loops. The separated fractions remain in the loops until mobile phase is used to send it to the NMR flow cell. After transfer to the probe, the valves divert the mobile phase and the HPLC pump is shut off, allowing the transferred sample to remain in the NMR probe. A loop collector may be viewed as a fraction collector; however, instead of using collection vials or tubes, the fractions are collected in pressurized loops. Although the system can be configured to allow each loop’s contents to be pumped into the NMR flow probe it can also be removed and used as a remote unit. If used off-line with a separate HPLC system, the loops may be filled and then the entire loop assembly can be transferred to the NMR system [24,25]. The loop volume capacity can be adjusted to a desired size by adjusting the tubing length while keeping the diameter fixed. The loop system typically uses multiport rotary valves located downstream from the LC detector; hence, the LC-detector signal can be used to activate the valves. The system can be programmed to trap multiple chromatographic peaks in the loops automatically—all under computer control (based upon the LC detector’s signal output). Loop collectors are useful when lengthy NMR data collection is required or when detectable amounts of material may be collected from a single chromatographic injection. In such cases, the isolated compound may be stored in a controlled environment without concern of decomposition from solid support or changes with respect to light or heat. A disadvantage of loop collection in LC-NMR is matching solvent composition. If solvent composition in the loop is significantly different from the mobile phase solvent that pushes the loop’s contents into the NMR probe, magnetic-susceptibility mismatches between the two solvent mixtures will result, causing shimming problems and broad lines. Possible solutions involve adjusting the loop volume to be larger relative to the flow cell volume to displace a different mobile phase. Alternatively, one may attempt to match the mobile phase with that of the solvent composition in the loop; however, this can be difficult to achieve. © 2012 Taylor & Francis Group, LLC

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3.5.3  Solid Phase Extraction The latest development in the field of hyphenated techniques is the use of a solid phase extraction (SPE) system as an interface between liquid chromatography (LC) and NMR. SPE combined with LC provides a system that enables peak collection of an analyte on a cartridge. As a compound is eluted from an HPLC column, it may be diverted and trapped on an SPE cartridge. The peak selection is typically done either by UV detection or by evaluation of MS spectra. The integration of SPE with flow injection NMR was first demonstrated by Griffiths and Horton [26] followed by de Koning et al. in 1998 [27]. Subsequently, numerous reports on the use of SPE-NMR have appeared in the literature [18,28–38]. For SPE, the trapping process involves adding water via a makeup pump to the mobile phase as it is eluted from the LC column (when reversed phase HPLC is used). Elution from the cartridge can occur via a separate pump to dispense stronger solvents that can transfer the analyte from the SPE cartridge. This process is illustrated in Figure 3.9. The SPE-NMR hardware may be viewed as a loop collector with an SPE cartridge spliced into the middle of the loop tubing. A makeup pump introduces water to the mobile phase as it leaves the LC column and enters the SPE cartridge. The SPE cartridge may be interfaced with an NMR flow probe to enable the sample to

SPE in LC-NMR Cartridge wash Water and ACN or MeOH

H2O Water addition

Dry and transfer into probe Deuterated solvents

600 MHz

Sample

Solvents salts buffers

Figure 3.9  Illustration of the interface of liquid chromatography (LC) and solid phase extraction (SPE) with NMR spectroscopy. Compound can be incrementally added to a cartridge. The cartridge can then be washed and then dried with nitrogen gas and the compound eluted from the cartridge with deuterated solvent. © 2012 Taylor & Francis Group, LLC

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be directed into a flow cell for NMR detection. A separate pump is used to transfer the deuterated solvent that elutes the analytes from the SPE cartridges through the capillary tubing directly into the NMR flow probe. In such cases, the eluting solvent is usually deuterated acetonitrile or methanol (CD3CN or CD3OD). The deuterated solvent provides a lock signal to prevent the frequencies from drifting during data acquisition and to address a dynamic range issue resulting from large proteosolvent peaks. The deuterated solvents may be stored over a stream of dry nitrogen gas to prevent absorption of water from the atmosphere. A stream of dry nitrogen gas is also used to dry the cartridges prior to eluting into the NMR probe with deuterated solvent. This drying will further reduce the large signal contribution from proteosolvents such as residual water and acetonitrile. Although large solvent peaks can be reduced using solvent-suppression pulse sequences, critical peaks from the sample may also be suppressed, thereby compromising structural analysis. Hence, minimization of proteosolvents from the NMR sample is good common practice. An important consideration with flow NMR is that the sample in the flow cell maintains uniform magnetic susceptibility. To achieve this, solvents in the sample must be homogeneous. If a solvent gradient exists, the line shape of the NMR signal will become broad. One advantage of the SPE method is that the analyte is dissolved in a single homogeneous deuterated solvent that transfers the compound as a concentrated fraction, thereby eliminating the magnetic susceptibility problem. Hence, SPE-NMR can successfully be used to concentrate and spectrally characterize compounds that may elute as broad chromatographic peaks with long retention times [34]. SPE also offers an advantage with respect to the integration of NMR and MS technologies. In particular, finding a solvent system that is compatible with both the gradient profile and columns used in the separation protocols for NMR and MS can be difficult. Additionally, use of the deuterated solvents that are desired in NMR analysis creates problems in the MS analysis where the analyte is subject to H/D exchange, resulting in a shift of one mass unit for every exchangeable hydrogen. With SPE, all chromatography may be performed using conditions compatible to MS analysis and without the need for deuterated solvents [39]. An additional advantage of SPE-NMR is that multiple trapping is possible. Although both the loop collector and SPE have the chromatographic step performed separately from the NMR analysis, the SPE system can trap peaks from multiple injections, allowing a single compound to be built up on a specified cartridge. This enhances the concentration of material sent to the flow cell and can be effectively used to trap impurities or low-level metabolites. Concentration in the 0.1% range relative to the major analyte may be isolated on an SPE cartridge with proteosolvents, dried, and then eluted with deuterated solvents. Full spectral characterization may then be possible on the sample once sufficient concentration is obtained [18,32]. It should be noted that since an SPE cartridge may be viewed as a “ministorage column,” one can consider the resulting elution step of SPE-NMR as just another form of chromatography where the sample stored on the SPE column may be eluted into a capillary tube for NMR evaluation or into a vial. Samples from SPE-NMR studies can also be recovered from an NMR flow probe at the end of the NMR © 2012 Taylor & Francis Group, LLC

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analysis by blowing them out of the probe into a vial or tube with nitrogen gas. Collected samples may then be dried and taken up in an alternate deuterated solvent for further evaluation under the control of the user. Hence, low concentrations due to limited on-column loading are eliminated with SPE [28]. While the SPE system offers a tremendous advantage in building sample concentration, retention on specific cartridge types is compound dependent. Finding a cartridge with the appropriate solid support for a particular compound or system type needs to be performed for each new compound. Method development cartridge trays are commercially available for this purpose. Some typical SPE cartridge support systems used in method development studies are given in Table 3.2.

Table 3.2 SPE Cartridge Selection for Method Development Type HySphere CN-SE

C2-SE

C8-EC-SE

C18-HD

Resin GP

Size 7 μm 7 μm 8 μm 7 μm 10–12 μm

Structure CN

Si

CH2

Si

CH2

Si

CH2

7

CH3

Si

CH2

17

CH3

H C

3

CH3

CH3

H C

H2 C

H C

CH3

H C Resin SH

25–35 μm

MM cation MM anion

10–12 μm 25–35 μm

CH3

Polymeric-based mixed-mode exchangers Polymeric-based mixed-mode exchangers

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In summary, the major advantages of SPE-NMR are as follows: • Chromatographic separation can be done with inexpensive, nondeuterated solvents or with additives that are not compatible with NMR spectroscopy. • Because no D2O is used in the eluent, no H–D exchange occurs during the chromatographic process, which could result in elimination of critical exchangeable protons needed for structure elucidation. • Only small amounts (approx. 300 μL) of deuterated solvents are required for the transfer. • The complete sample can be eluted in a small volume ( = < 1 σ* > / 1 σ

(4.7)

where the brackets represent average quantities. The authors concluded that resolution is only slightly compromised if at least three to four samples are collected across twice the peak width (i.e., 8 1 σ), thus justifying an intuitive assertion by Holland and Jorgenson [31]. Panel (a) of Figure 4.4 is a graph of β for sample numbers N of 1–5, with the left- and right-most abscissas corresponding to in-phase and out-of-phase sampling. Panel (b) of Figure  4.4 is a series of two-dimensional separations with different sampling times. It is clear the apparent first-dimension peak width increases with increasing sampling time. This illustration of the effect of undersampling is highly analogous to that shown in Figure 4.2. Seeley examined the effect on β of sampling time and phase, as well as the duty cycle (i.e., the fraction of the sampling interval in which the effluent is collected) [32]. By expressing the average concentrations of a sampled first-dimension © 2012 Taylor & Francis Group, LLC

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Peter W. Carr, Joe M. Davis, Sarah C. Rutan, and Dwight R. Stoll 5

4

β 3

1

2

2

3

4

5 0.20 0.40 0.60 0.80 Fraction of Phase Retarded by –41σ/N (a)

1 0.00

0

1.00 min

1.50 min

0.2 0.4 0.6 0.8 GPC (min)

0.7 0.9 1.1 1.3

2.00 min

3.00 min

4.00 min

1.2 1.4 1.6 1.8

1.2 1.4 1.6 1.8 GPC (min) Second Dimension (b)

1.2 1.4 1.6 1.8

35 0.0 0.2 0.4 0.6 0

HPLC (min)

First Dimension

HPLC (min)

0.67 min

1.00

35

Figure 4.4  (a) Graph of peak-broadening factor β versus the fraction of retarded phase for N second-dimension fractions, as calculated by Murphy et al. (b) Separation of poly(ethylene glycol) and Brij surfactants by LC × LC (first dimension, HPLC; second dimension, gel permeation chromatography). Different sampling intervals ts are reported in the panels. (Reprinted with permission from Murphy, R. E. et al. 1998. Analytical Chemistry 70:1585–1594, ©1998 American Chemical Society.) © 2012 Taylor & Francis Group, LLC

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–3

–2 –1

0

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d 1.0 0.8 0.5 0.1

1.6

β

1.8

16

1 4

φ

(a)

1

2

ts/1σ

3

(b)

Figure 4.5  (a) Graph of peak-broadening factor β versus phase angle ϕ for different dimensionless sampling times ts /1σ. Phase angle varies from –π to π. Computations are based on the method of Seeley. (b) Graph of average peak-broadening factor versus ts /1σ for different fractional duty cycles d. (Panel (b) reprinted from Seeley, J. V. 2002. Journal of Chromatography A 962:21–27, ©2002, with permission from Elsevier.)

Gaussian peak by concentration pulses (like those in Figure 4.3), he calculated β as a function of the sampling time, ts, divided by 1σ. For any ts / 1 σ ratio, he found that β decreases with decreasing duty cycle, and at any duty cycle, β is smallest for inphase sampling and largest for out-of-phase sampling. The phase-averaged value of β, , decreases with duty cycle and, for a 100% duty cycle, agrees with the results of Murphy et al. [28]. Panel (a) of Figure  4.5 shows for the first time the variation of β with phase angle ϕ for different ts  / 1 σ and at a 100% duty cycle (Seeley reported results for only ts  / 1 σ = 2). The β value becomes increasingly sensitive to phase as ts  / 1 σ increases. Panel (b) of Figure 4.5 is a graph of versus ts  / 1 σ for different duty cycles. Seeley concluded that is less than 1.3 when ts  / 1 σ < 2. Blumberg and co-workers provided insight into β using signal-processing methods. First, Blumberg reported that the peak sampling process in online two-dimensional chromatography could be mathematically interpreted as a moving-average filter, followed by ideal sampling and subsequent peak reconstruction by interpolation [33]. Each of these processes adds to the inherent peak variance a term equal to ts2 /12 (see later discussion). Blumberg et al. then expanded on that work and derived the simple equation [34]



β B = 1 + 1 (ts /1 σ )2 4

(4.8)

where the subscript “B” denotes a representative (but not necessarily average) β value, for which phase is not considered. The theory behind Equation 4.8 is reviewed in a third paper, which contains Figure 4.6 [35]. As shown therein, the sampling of a 1D peak can be viewed as the © 2012 Taylor & Francis Group, LLC

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Snapshot sampler

Accumulator

∆ts

From 1st-dimension column

Into 2nd-dimension column t

0

(a)

Boxcar filter

Boxcar filter

∆ts

Sequence of data points 0

∆ts t

0

Reconstructed (analog) signal t

(b)

Figure 4.6  The generation of a linearly interpolated peak by the sampling and filtering of a Gaussian peak. (From Blumberg, L. M. 2008. Journal of Separation Science 31:3358–3365, ©Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.)

action of a boxcar-type accumulator (integrator) of duration ts, which broadens the peak prior to its discrete sampling by a snapshot sampler (or Dirac impulse train). The resulting sequence of discrete concentrations is then filtered by two boxcar filters, each of duration ts. The first produces a histogram-like peak and the second gives a linearly interpolated peak. The mathematics underlying these actions is convolution, with the accumulator and both filters making a contribution of ts2 /12 to the peak variance. The variances are additive, with the total sampling-induced peak variance being 3ts2 /12 = ts2 /4 , producing Equation 4.8. The additional variance ts2 /4 is independent of peak shape (e.g., Gaussian or otherwise). By simulation, Blumberg showed his βB value lay between β values for in-phase and out-of-phase sampling. In contrast to all of the preceding methods, which focus on the broadening of a single peak, Davis, Stoll, and Carr estimated the average peak-broadening factor at different ts /1σ values by using statistical-overlap theory (SOT) simulations of comprehensive two-dimensional separations containing bi-Gaussian peaks [36]. The study differed from its predecessors by simulating the effect of undersampling on 1σ by undersampling multiple randomly spaced peaks, and it included the impact of the distribution of peak heights (exponential). By use of SOT, the authors imposed a simple meaning on : A two-dimensional separation of randomly positioned peaks sampled at the dimensionless rate ts /1 σ has the same number of maxima as an otherwise identical separation of very rapidly sampled peaks having the broadened first-dimension standard deviation © 2012 Taylor & Francis Group, LLC

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8

6 4 2 0

0

4

8 ts/1σ

12

16

Figure 4.7  Graph of versus ts /1σ. Points are SOT determinations of ; solid curve is Equation 4.9 with κ = 0.214. Also shown are predictions of Blumberg (— — —) and Seeley (- - - - - - -).

1σ. Figure 4.7 is the graph of versus ts /1 σ thus determined, with the SOTbased values represented by points. The solid curve is a fit of the empirical function (proposed independently of Blumberg et al. [33,34]):



< β >= 1 + κ (ts /1 σ )2

(4.9)

with κ = 0.214 ± 0.010 . For comparison, the βB value predicted by Blumberg et al. [33,34] and the average predicted by Seeley for a 100% duty cycle [32] (equal to the prediction of Murphy et al. [28]) are also shown. Here, the Seeley result was determined by averaging over 101 phase angles; it differs slightly from the Monte Carlo calculation of Davis et al. [36], which has a small bias. The SOT-based and βB are similar because a linearly interpolated peak and the first dimension of a biGaussian peak roughly resemble one another. Both result in larger values of β than the prediction of Seeley for ts /1 σ values greater than 4. Equation 4.9 does not fit Seeley’s results well (R = 0.996), but the associated κ coefficient is 0.117, or about two times smaller than κ values obtained by Davis et al. and by Blumberg. Other SOT-based determinations of are given later, as is a table of relevant κ values (Table 4.2). Vivó-Truyols, van der Wal, and Schoenmakers [37] interpreted the 2D separation as a detector of each first-dimension sample, with a sampling frequency of 1/ts. This interpretation led them to postulate Equation 4.9 on a theoretical basis, with the coefficient κ equal to 1/12 under ideal conditions, 1/4 as described by Blumberg [33,34], or 0.214 as described by Davis et al. [36]. These authors used Equation 4.9 (with κ  =  0.214) and an expression for second-dimension injection band broadening to study peak capacities based on Pareto optimization. The results of this work will be discussed at some length in Section 4.4. In related work, the group of Guiochon included the effect of on the peak capacity and analysis time of LC × LC [38] and off-line LC × LC [39]. © 2012 Taylor & Francis Group, LLC

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The undersampling correction factor used in those papers is simply a reformulation of Equation 4.9, with the value of κ determined as exactly 0.214. The group also addressed the effect of apparent diffusion on the increased 1D peak width during stop-and-go 2D-LC [40]. Two general comments regarding the body of work described previously merit discussion here. First, the various estimates of differ because different approaches were used to determine it. As observed by Davis et al. [36], a severely undersampled peak does not satisfy the Nyquist theorem and therefore has no unique analog reconstruction of the 1D peak profile from the digital data. Second, the relationship between the effective 1D peak capacity and the number of fractions collected is the subject of some debate. Some researchers suggest that the 1D peak capacity cannot exceed the number of fractions taken from the first dimension [8,9,38], with the implication that the corrected first-dimension peak capacity, 1nc′ , defined by Horie et al. [41] as 1



nc′ = 1nc /< β > ,

(4.10)

has a limited range of validity.

4.2.2  Effect of Undersampling on LC × LC Peak Capacity As will be described in Section 4.4.1, the second-dimension peak capacity 2 nc increases monotonically with the amount of time allotted to carry out the separation. Thus, 2 nc increases as ts increases. However, because sampling broadens the first-dimension peaks, the corrected first-dimension peak capacity 1nc′ decreases as ts increases, causing opposing trends in 1nc′ and 2 nc. The result is that optimal values exist for the sampling time and the corrected two-dimensional peak capacity nc′,2 D [41], previously reported as Equation 4.3:

nc′,2 D = 1nc′ 2 nc = 1nc 2 nc /< β >

(4.11)

The characteristics of the optima depend on what equations are used for 1nc, 2nc, and . Davis, Stoll, and Carr [42] showed by simulation that the number of maxima in a twodimensional separation and nc′,2 D are related by a monotonic function, regardless of the values of the individual factors, 1nc and 2nc. The factor expressed by Equation 4.9 is needed to produce this relationship. They also showed that separations of peaks having weakly correlated 1D and 2D retention times produce two-dimensional separations consistent with the SOT-imposed interpretation of .

4.2.3  Additional SOT-Based Determinations of Although most aspects of undersampling are understood, subtle questions remain. Two are answered here for the first time. First, is the value of mitigated by the © 2012 Taylor & Francis Group, LLC

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second-dimension separation, beyond that expected from the additional peak capacity 2 n ? This is possible, because the second dimension of separation increases the numc ber of observed peaks (maxima), thereby possibly affecting the SOT determination of κ in Equation 4.9 in a way that is not possible for a one-dimensional separation. Second, what is the influence on of the type of distribution of peak heights? Both questions were addressed by interpreting the results of simulations of multipeak separations using SOT. Three cases were considered: (1) random one-dimensional peaks with exponential heights, (2) random one-dimensional peaks with constant heights (i.e., all components have the same height or concentration times detector sensitivity), and (3) random two-dimensional peaks with constant heights. The interpretations depend on the relationship between two SOT attributes: the average minimum resolution Rs* and the saturation α. This relation is known for random one-dimensional peaks with exponential heights [43] but not for random one- and two-dimensional peaks with constant heights. These relationships were determined empirically using a procedure (explained elsewhere) in which arbitrarily defined α and Rs* values are corrected by interpreting simulation results by theory [44]. In the procedure, 500 one-dimensional simulations with 10,000 peaks and 50 two-dimensional simulations with 2,000 peaks, with an aspect ratio 1nc / 2 nc of one, were used. For different ts /1 σ values, 50 two-dimensional separations of random peaks with constant heights were mimicked as in Davis et al. [36] for four peak numbers between 100 and 400 and seven peak-capacity combinations. Using a similar algorithm, one-dimensional separations of random peaks with exponential or constant heights were mimicked for eight peak numbers between 50 and 400 and four 1nc values. The peak capacities are reported in Table 4.1. Values of were calculated as in Davis et al. [36], except that one-dimensional SOT was used to interpret

Table 4.1 Peak Capacities at Unit Resolution for 1nc and 2nc of Sampled Simulations with Exponential (E) and Constant (C) Peak Heights 1D Separations nc , E 2,560 1,280 640 320 1

nc, C 1,280 640 320 160

1

2D Separations, C nc 20 40 20 80 20 10 10

1

nc 20 20 40 40 10 20 10

2

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6 4 2 0

0

4

8 ts/1σ

12

16

Figure 4.8  Graph of versus ts /1σ for random one-dimensional peaks with constant heights (◼), random one-dimensional peaks with exponential heights (⚫), and random twodimensional peaks with constant heights (▲). Curves are fits to Equation 4.9. Fitting coefficients κ are reported in Table 4.2.

the simulated one-dimensional separations. The α − Rs* curves for constant peak heights are not shown so as to conserve space; interested readers can contact the author (JMD) for details. Figure  4.8 is a graph of versus ts /1 σ determined from the simulations. Standard deviations are not shown but the largest RSD is only 11.3%. The curves are weighted fits to Equation 4.9, which describes the data well. The least-squares fitted coefficients κ are reported in Table 4.2, as are other κ values discussed previously. Given the same type of peak-height distribution, κ is significantly smaller for the two-dimensional separation than the one-dimensional separation. This shows that the two-dimensional separation is considerably less sensitive to the undersampling effect than is the one-dimensional separation. That is, a significant fraction of the peak maxima that would be lost due to undersampling the Table 4.2 Coefficients κ in Equation 4.9, as Determined with Exponential (E) and Constant (C) Peak Heightsa 1D separation, C 1D separation, E 2D separation, C 2D separation, E a

0.354 ± 0.009 0.301 ± 0.008 0.233 ± 0.015 0.214 ± 0.010 [36]

κ for Blumberg prediction βB [33,34]: ¼; κ for Seeley prediction [32] in Figure 4.7: 0.117.

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first dimension are recovered by resolving the maxima in the second dimension. For the same dimension of separation, κ is significantly smaller for exponential peak heights than for constant peak heights. We believe that the fact that the twodimensional SOT-determined κ values are similar to the value, 1/4, predicted by Blumberg [33,34] is happenstance. However, the issue is of marginal importance and it probably will not make any real difference if we take the two-dimensional value of κ as 0.214 or 0.25.

4.3  Orthogonality, Practical Peak Capacity, and Fractional Coverage The evaluation of orthogonality in two-dimensional separations is a vital but elusive goal. Although most researchers agree that orthogonality can be achieved only if separation mechanisms are unrelated, there is little consensus on conceptual models or practical metrics of the degree of orthogonality. Schoenmakers et al. observed that part of the difficulty occurs because orthogonality has different meanings in mathematics, statistics, and analytical chemistry [26]. A consequence of nonorthogonality is that the total two-dimensional peak capacity is not available for use because the entire separation space has not been effectively utilized, leading to a loss of resolution and identification power. Various metrics (e.g., practical peak capacity and fractional [or surface] coverage) have been proposed to describe the used portion of the two-dimensional space. As with orthogonality, little consensus exists regarding the best metric.

4.3.1  Models of Orthogonality Giddings [45] explained retention time correlations in terms of sample dimensionality, or the number of independent variables needed to identify the components of a sample (e.g., carbon number, number and location of multiple bonds, and number of repeat units in block copolymers). When the sample dimensionality exceeds the number of independent dimensions of separation, insufficient information exists to determine the sample variables and the separation is disordered. If the sample dimensionality is less than or equal to the number of separation dimensions, the sample variables are determined and the separation has order (i.e., correlation and structure). Figure 4.9 shows a predicted two-dimensional graph of correlated peak coordinates that depend on two sample variables. Since the number of sample variables exceeds the number of dimensions of a one-dimensional separation (one), the reconstructed one-dimensional separation projected along the first-dimension axis is disordered. Liu, Patterson, and Lee [46] proposed a geometric description of orthogonality based on factor analysis. The authors calculated a peak-spreading angle equal to the arc cosine of the off-diagonal entry of the 2 × 2 correlation matrix computed from standardized 1D and 2D peak coordinates. This entry is the same as the linear correlation coefficient r, which varies in magnitude from zero for an orthogonal separation to one for a correlated separation. Clearly, the peak-spreading angle is a statistical metric. © 2012 Taylor & Francis Group, LLC

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x2

3

π X1 = 0.5p1 + — p2 + 0.01p1 p2 10 1 X2 = 0.2p1 + — p2 π

2

1

3

4

5 x1

6

7

Figure 4.9  Graph of correlated two-dimensional peak coordinates x1 and x2, which depend on sample variables p1 and p2 as shown. Projected one-dimensional coordinates along axis x1 are disordered. (Reprinted from Giddings, J. C. 1995. Journal of Chromatography A 703:3–15, ©1995, with permission from Elsevier.)

Slonecker et al. [47] applied information theory to two-dimensional separations as a metric of orthogonality. The informational entropy of Shannon, calculated from the probabilities of peak coordinates lying within specific ranges of retention times, was evaluated for different one-dimensional separations and hypothetical twodimensional separations formed by pairing them. The difference in information content was related to the mutual information, informational similarity, and synentropy, which are metrics of correlation. Near-orthogonal separations have very low or zero similarity, whereas nonorthogonal ones have high similarity and moderate to high synentropy. The authors made calculations for 105 stationary-phase combinations. Only a few combinations produced near-orthogonal separations. The authors noted that their predictions were sample specific. Jandera and co-workers studied in detail the orthogonality of separations of twoblock copolymers [22,48–52]. The solutes’ retention factors on two columns were related to differences among selectivity factors of the repeat units. In this case, an orthogonal separation has selectivity in one dimension for one type of repeat unit but not the other, whereas the other dimension has selectivity for the second repeat unit but not the first. This orthogonality assessment is related to Giddings’s sample dimensionality [45]. Panels (a) and (b) of Figure 4.10 show the distribution of retention factors for correlated and near-orthogonal separations [51]. Ryan, Morrison, and Marriott [53] observed that in the absence of wraparound, the maximum space used by a two-dimensional separation is bound in the first dimension by the full retention range and, for any second-dimension sample, is bound by the interval between the second-dimension void time and the 2tR of the most retained peak. The authors argued that orthogonality increases as the gap between these bounds increases. Gilar et al. [54] proposed an equation for a geometric orthogonality, as defined by a two-dimensional space having equal numbers of peak-capacity units in both dimensions. For equal numbers of peak coordinates and peak-capacity units, the equation equaled zero, when coordinates spanned the separation diagonal, and equaled one © 2012 Taylor & Francis Group, LLC

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nEO

10

4

kNP1

8 3

6 nPO 10 12 14 16 2

4 2 0

9

kNP1

7

1

0 0.5

0.7

0.9 1.1 kNP2 (a)

1.3

1.5

nPO 5 6 7

8

3

nEO 14 12

1

8

5

0.5

1.0

9

1.5 2.0 kRP (b)

2.5

3.0

Figure 4.10  Capacity factors k of ethylene glycol-propylene glycol (EO-PO) (co)oligomers on (a) two normal-phase (NP) columns and (b) normal-phase and reversed-phase (RP) columns for different numbers of EO monomers, n EO, and PO monomers, nPO. In panel (a), strong correlation of k causes elution near the separation diagonal. In panel (b), elution from the RP column is controlled by nPO and is independent of nEO. (Reprinted from Jandera, P. et al. 2005. Journal of Chromatography A 1087:112–123, ©2005, with permission from Elsevier.)

when coordinates were randomly distributed throughout the space. Watson, Davis, and Synovec [55] discussed problems with the equation at the limits, zero and one, and made corrections to the latter. They suggested that orthogonality is improved by maximizing the fractional coverage (i.e., the fraction of occupied space) at a given saturation or total peak capacity. Poole and Poole [56] applied the solvation parameter model to calculate the orthogonality of two GC stationary phases from either the Euclidean distance between five solute system constants or the cosine of the hyperangle between the lines representing the phases in a five-dimensional space. The method has also been used successfully with liquid-based separations (e.g., microemulsions, micelles, liposomes, and polymeric phases [57–59]) and could be applied to LC × LC. Bedani, Kok, and Janssen [60] defined an orthogonality metric between 0 and 1, equal to the occupied fraction of a two-dimensional separation having 1D and 2D axes scaled in units of percentage organic modifier. Over the entire first dimension, © 2012 Taylor & Francis Group, LLC

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tR (2D) (min)

5 4 3 2 1

First peak Last peak

8 13 Time of Fraction (1D) (min) (a)

3

18

45.0

%AcN (2D)

35.0

O = 45% 2∆AcN

25.0

First peak Last peak

15.0 5.0 5.0

10.0

15.0 20.0 %AcN (1D) (b)

25.0

30.0

Figure 4.11  Orthogonal metric of Bedani et al. Panel (a) shows retention times of first and final peaks in representative second-dimension samples. In panel (b), the time axes are rescaled as percentage organic modifier (here, acetonitrile). The lines connecting the upper and lower sequence of points define a space whose fraction of the total space is the orthogonality O. (Reprinted from Bedani, F. et al. 2009. Analytica Chimica Acta 654:77–84, ©2009, with permission from Elsevier.)

simple boundaries (e.g., lines) defined the fraction of occupied space between the first and last peaks of 2D separations. Figure 4.11 shows the fraction of space thus described. The occupied space is similar to that proposed by Ryan et al. [53], but the lower bound of the second dimension is determined by the first eluting peak, not the void time. Schure [61] introduced the dimensionality of separation D as a dimensionally invariant orthogonality metric that is independent of the separation size, the number of dimensions, and the angle between retention vectors. The dimensionality is based on a fractal scaling law and is measured by partitioning normalized retention times among a series of variably sized “boxes” (e.g., interval segments, squares, and cubes in one-, two-, and three-dimensional separations, respectively) and counting the number of “boxes” containing retention times. Schure argued that D equals the lower bound of Giddings’s sample dimensionality [45]. Figure  4.12 © 2012 Taylor & Francis Group, LLC

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Amplitude

Amplitude

D = 2.00

200

800

1,000

1,000 800 Ti 600 m e ( 400 se 200 c) 00

600

200

800

1,000

400 (sec) Time

(a)

(b)

D = 0.71

D = 1.78 Amplitude

0

600 400 (sec) Time

Amplitude

1,000 800 Ti 600 m e ( 400 se 200 c) 0

1,000 1,000 Ti 800600 1000.0 T 800 m 800.0 im 600 e ( 400 600.0 se e ( 400 400.0 c) 200 se ec) 0 0.0 200.0 c) 200 Time (s 0

(c)

0

200

800 600 400 ) c e s ( Time

1,000

(d)

Figure 4.12  Values of separation dimensionality D calculated by Schure from simulations of (a) a uniformly ordered two-dimensional separation, (b) a uniformly ordered two-dimensional separation spanning the diagonal, (c) a random two-dimensional separation spanning the diagonal, and (d) a random two-dimensional separation. (Reprinted from Schure, M. R. 2011. Journal of Chromatography A 1218:293–302, ©2010, with permission from Elsevier.)

shows simulations of ordered and disordered two-dimensional separations in which D varies from 0.71 to 2. Of all these orthogonality metrics, the separation dimensionality of Schure [61] is perhaps the best. It is simple to calculate, well rooted in other scientific disciplines (as opposed to ad hoc models limited to separation science), applicable to any number of separation dimensions, and easy to interpret. The first three attributes also apply to information theory [47,62], but its predictions are not as easily interpreted.

4.3.2  Applications of Orthogonality Metrics in Two-Dimensional Separations A few of the models discussed previously have been used by researchers other than the original authors to assess orthogonality in both LC × LC and GC × GC. Some assessments are based on the bound space of Ryan et al. [53] (e.g., Cordero et al. [63]) and information theory (e.g., references 63–67). However, the most common © 2012 Taylor & Francis Group, LLC

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orthogonality metric is the linear correlation coefficient r (or, equivalently, the peakspreading angle) (e.g., references 49, 63–75). Since r is a statistical metric, not a chemical one, it has limitations. Van Gyseghem et al. [76] observed that misleadingly small r values can be produced when only a small fraction of peak coordinates lie far from the separation diagonal. Stoll et al. [21] noted that a small r does not imply a full coverage of the twodimensional space, since 2 tR can be restricted to a narrow range in the second dimension. Watson et al. [55] observed that r approaches zero for both a randomly disordered two-dimensional separation and a fully ordered one in which peaks are centered in peak-capacity units like checkers on a checkerboard, even though the second separation is better. Dumarey, Vander Heyden, and Rutan [77] noted that low r values do not imply high identification power, since r measures separation differences and not separation quality. Blumberg and Klee [78] observed that the orthogonality of displacement mechanisms is different from the statistical uniformity of peak coordinates. In contrast, many other metrics have been used to evaluate the orthogonality (i.e., similarity vs. dissimilarity) of multiple one-dimensional chromatographic systems, which are not coupled together. In addition to r [62,76,79–82], assessments have been made using dissimilarity graphs [79,82], principal component analysis [76,83], dendrograms [62,76,79,82], the hydrophobic subtraction model [83,84], stationary-phase triangles [85], KUL (Katholieke Universiteit Leuven) [83], the orthogonal projection approach [79], the generalized pairwise correlation method [79], auto-associative multivariate regression trees [62,79], the weighted pair group method using arithmetic averages [79], the Kennard and Stone algorithm [79], Spearman’s rho [81], Kendall’s tau [81], Williams’s t-test [81], the conditional Fisher’s test [81], McNemar’s test [81], and the chi-square test [81]. In some cases, predictions have been visually encoded using color maps for easy visual recognition of patterns [62,76,79]. The preceding citations are only representative; other references are given in the articles. Only a few of these methods have been applied to LC × LC. Two studies based on multiple techniques of orthogonality assessment in LC × LC merit mention. Jandera et al. [70] used similarity dendrograms based on interaction indices and linear free-energy relationships, and correlation coefficients between retention factors to find orthogonal combinations of six columns for the LC × LC of phenolic acids and flavonoids. Dumarey et al. [77] used the hydrophobic subtraction model, correlation coefficients, information theory, the number of resolved peaks, and multivariate selectivity to find orthogonal combinations of 14 columns. They judged the multivariate selectivity [86,87] to be the best metric.

4.3.3  Practical Peak Capacity and Fractional Coverage Liu et al. [46] introduced the term “practical peak capacity” and defined it as the “available area determined by the retention correlation in the space.” It was calculated as that part of the total peak capacity lying between two vectors originating at the lower spatial boundary and spanned by a specific orientation of the peak-spreading angle, calculated as described previously. Figure 4.13 shows the fraction of peak capacity spanned by the peak-spreading angle. © 2012 Taylor & Francis Group, LLC

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Effective Area NP

N2

A

γ β α´

C

α N1

Figure 4.13  Practical peak capacity of Liu et al. The peak-spreading angle expands into the occupied checkered area. (Reprinted with permission from Liu, Z. et al. 1995. Analytical Chemistry 67:3840–3845, ©1995 American Chemical Society.)

Several papers have reported practical peak capacities thus determined [64–67,71,73,75]. However, the two vectors in question are n-dimensional, where n is the number of peak coordinates used in calculating the correlation coefficient [88]. Although it is true that the cosine of the angle between these vectors equals r, it does not follow that the image of these vectors onto the two-dimensional separation space preserves the same angle. This metric is examined further later (see Figure 4.16). Jandera et al. [22,52] proposed that the peak capacity of a correlated two-dimensional separation is the weighted sum of an orthogonal contribution, given by the product rule 1nc 2 nc, and a serial contribution equal to the square root of the sum of squares of 1nc and 2 nc:



(1 − z ) 1nc 2 nc + z

n + 2 nc2

1 2 c

(4.12)

The authors suggested that repeat units could be the basis of the weighting factor z, which is the absolute value of the ratio of the logarithms of the separation factors for both columns, as calculated from compounds differing by a single repeat unit. Gilar et al. [54] proposed a geometric description of practical peak capacity based on the superposition of a rectangular grid on reduced two-dimensional peak coordinates. Different suggestions for grid-element size were considered (e.g., the normalized peak area and the peak-capacity unit). The authors defined the practical peak capacity as the product of the total peak capacity and the surface coverage, or the fraction of grid elements containing peak coordinates. Figure 4.14 shows the superposition of a 10 × 10 grid on 100 randomly positioned coordinates, which occupy 64 elements. Here, the surface coverage is 64%. A further examination of this metric is presented later. Watson et al. [55] described the same metric by the words “fractional coverage” instead of surface coverage. © 2012 Taylor & Francis Group, LLC

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Figure 4.14  Practical peak capacity of Gilar et al. Squares represent peak-capacity units; shaded squares contain one or more peak coordinates. (Reprinted with permission from Gilar, M. et al. 2005. Analytical Chemistry 77:6426–6434, ©2005 American Chemical Society.)

Jandera et al. [51] reported an expression for the unused space in each 2D separation of two-block copolymers. It was related to the retention volume of the solute having the fewest repeat units controlling the 2D retention. Stoll pioneered the description of fractional coverage by enclosing all twodimensional coordinates by an intuitively shaped polygon conforming to the boundaries of peak-capacity units. An example polygon is shown in Figure 4.15 [42]. The ratio of the number of enclosed units to the total peak capacity determined the fractional coverage. Davis [89] used statistical-overlap theory to interpret simulations of bi-Gaussian peaks that were randomly positioned in simple nonrectangular geometries mimicking the boundaries of correlated two-dimensional separations. He found that the bound area could be interpreted as a practical peak capacity. The relations between random peak coordinates in these geometries and the linear correlation coefficient r were derived. Panels (a–c) of Figure 4.16 are graphs of three geometries presented in reduced coordinates, for which r = 0.75. Different r values were obtained as the angles between edges were changed. Panel (d) of Figure 4.16 is a graph of the fraction of the coordinate-occupied space versus r, shown here for the first time. The curve is the fraction of coordinate-occupied space, as predicted from the practical peak capacity of Liu et al. for equal 1nc and 2 nc [46]. The predicted fraction tracks the actual ones but overestimates them. Bedani et al. [60] identified the occupied peak capacity as the product of 1nc 2 nc and their orthogonality metric, which was discussed previously. Since this metric © 2012 Taylor & Francis Group, LLC

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18 16 14 12 10 8 6 4 2 0

0

5

20 10 15 1st Dimension Time (min)

25

30

Figure 4.15  Practical peak capacity of Stoll. Simple polygon is superposed around peak coordinates. (Reprinted with permission from Davis, J. M. et al. 2008. Analytical Chemistry 80:8122–8134, ©2008 American Chemical Society.)

is the occupied fraction of a two-dimensional separation having 1D and 2D axes rescaled in units of percentage organic modifier (see Figure 4.11), it also measures fractional coverage. The product of this metric and 1nc 2 nc could be interpreted as a practical peak capacity. 4.3.3.1  Combined Effect of Undersampling and Fractional Coverage on Two-Dimensional Peak Capacity Stoll et al. [29] used experimental one- and two-dimensional separations of a metabolomics sample to compare the resolving power of one- and two-dimensional separations, as evaluated by the number of maxima in the chromatograms and estimates of the effective peak capacity, reported before as Equation 4.2.

nc∗,2 D = 1nc 2 nc fcov /

(4.13)

With fcov computed by the method of Gilar et al. [54] and expressed by Equation 4.9 (κ = 0.21), the authors found that two-dimensional chromatograms of a corn-seed extract produced greater numbers of observed maxima and peak capacities than did one-dimensional chromatograms for separations exceeding 5 min; these trends were reversed at shorter times. This work and a related study are described in more detail in Section 4.6. Equation 4.13 has been reported elsewhere, but without specific determination of fcov [40,90]. 4.3.3.2  Analogies to Practical Peak Capacity and Fractional Coverage in Ecology Ecologists have applied and developed methods to calculate the “area traversed by the individual in its normal activities of food gathering, mating, and caring for young” [91]. This area is called the “home range” or “utilization distribution,” © 2012 Taylor & Francis Group, LLC

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1 r = 0.75

0.6 0.4 0.2 0

0

0.4

0.2

0.4 0.6 0.8 Fraction of 1nc (a)

0

1

0

0.2

0

0.2

0.4 0.6 0.8 Fraction of 1nc (b)

1

Occupied Area/Total Area

1 r = 0.75

0.8 Fraction of 2nc

0.6

0.2

1

0.6 0.4 0.2 0

r = 0.75

0.8 Fraction of 2nc

Fraction of 2nc

0.8

0

0.2

0.4 0.6 0.8 Fraction of 1nc (c)

1

0.8 0.6 0.4 0.2 0

0.4

r

0.6

0.8

1

(d)

Figure 4.16  (a–c) Nonrectangular geometries containing random peak coordinates with correlation coefficient r = 0.75. (d) Graph of the fraction of coordinate-occupied area in panels a (▲), b (⚫), and c (◼) versus r. Curve is fraction of coordinate-occupied area calculated from the peak-spreading angle of Liu et al. for equal 1nc and 2 nc [46]. (Panels a–c modeled after ones in Davis, J. M. 2008. In Multidimensional Liquid Chromatography: Theory and Applications in Industrial Chemistry and Life Sciences, ed. S. A. Cohen and M. R. Schure, 35–58. New York: John Wiley & Sons.)

depending on the calculation. In general, animal positions are represented by points in a two-dimensional plane, which are grouped to get an area. The methods of grouping include the minimum convex polygon [92], convex hull peels [93], parametric approaches based on least-squares [94,95], harmonic means [96], kernels [97–102], Monte Carlo simulation [103], α-hulls [104], nearest-neighbor clusters [105], nearest-neighbor convex hulls [106], and local convex hulls [107]. In all methods, a smoothing parameter is used to determine the amount of area associated with each point. For example, with kernels it is common to associate a bi-Gaussian of unit volume with each point; the width of the bi-Gaussian is chosen to minimize the mean integrated square area. Figure 4.17 shows animal positions and contour lines of an area thus determined [98]. The similarity between these contour lines and the footprint of a two-dimensional separation, like those in panel (b) of Figure 4.4, is striking. © 2012 Taylor & Francis Group, LLC

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163

6 km

N

Figure 4.17  Kernel estimate of area occupied by single lion, monitored every 2 days. Contours represent 75% isopleths. Note similarity to footprint of two-dimensional separation. (Reprinted with permission from Hemson, G. et al. 2005. Journal of Animal Ecology 74:455–463, ©2005 with permission from John Wiley & Sons.)

Davis suggested that the practical peak capacity could be calculated as the ratio of the area determined by these methods and the area of a peak-capacity unit; he suggested that the fractional coverage could be calculated as the ratio of this practical peak capacity and the total peak capacity [108]. Semard et al. put these ideas into use by calculating the occupied separation space in GC × GC with convex hulls [109]. Alternatively, a simpler adaptation of the kernel method is to use the bi-Gaussian-­ like peaks of the two-dimensional separation itself, with the footprint taken at some fraction of the maximum peak height (e.g., 5% or 10%). If the peaks are severely broadened by undersampling the first dimension, this will cause some overestimation of the coverage. This is similar to an idea proposed but not pursued by Gilar et al. [54]. 4.3.3.3  Reexamination of the Fractional-Coverage Method of Gilar et al. The dependence of the fractional coverage fcov on smoothing parameters extends even to the promising method of Gilar et al. [54], as shown here for the first time. As reported by the researcher, the fraction of occupied peak-capacity units decreases with increasing unit number and decreasing unit size. This variation is shown in panels (a) and (b) of Figure 4.18. Although both panels contain the same coordinates, © 2012 Taylor & Francis Group, LLC

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0.8

0.8

Reduced 2nd Dimension

Reduced 2nd Dimension

1

0.6 0.4

0.4 0.2

0.2 0

0.6

0

0.2

0.4 0.6 0.8 Reduced 1st Dimension

1

0

0

(a)

1

0.6 fcov

Filled Points D/41o = 50 D/42o = 25

1

D2D/161o2o = 500

0.6

m = 400

2

fcov 0.4

m = 250 0.2

0.2 0

1

D2D/161o2o = 2000

m = 100 0.5

1

(b)

m = 550

1

0.4

0.4 0.6 0.8 Reduced 1st Dimension

0.8

Open Points 1 D/41o = 25 2 D/42o = 50

0.8

0.2

1

1

Rs = 2Rs

(c)

1.5

2

0

0.5

1

1.5

2

1

Rs = 2Rs

(d)

Figure 4.18  (a) Reduced GC × GC coordinates. (Adapted from Davis, J. M. et al. 2008. Analytical Chemistry 80:8122–8134.) For the 25 superposed peak-capacity units, fcov = 0.96. (b) As in panel (a) but for 2500 peak-capacity units and fcov = 0.15. (c) Graph of fractional coverage fcov versus resolution 1Rs = 2 Rs for m random peaks and various assignments 1D/4 1σ and 2D/4 2σ. d) As in panel (c) but for the 598 correlated coordinates in panels (a) and (b), and various assignments 1D/4 1σ and 2D/4 2σ having the product 500 or 2,000. Legend of (1D/4 1σ, 2D/4 2σ) values for the product 500: ⃝ (50, 10); ⃞  (42.2, 11.9); ⃟  (34, 14.7); × (26, 19.2); + (18, 27.8); ⃤ (10, 50). Legend of (1D/4 1σ, 2D/4 2σ) values for the product 2,000: ⃝ (150, 13.3); ⃞  (120, 16.7); ⃟  (90, 22.2); × (60, 33.3); + (40, 50); ⃤ (26.7, 75); ▽ (13.3, 150).

fcov = 96% for the 25 peak-capacity units in panel (a), whereas fcov = 15% for the 2,500 peak-capacity units in panel (b). Clearly, any metric that depends on the grid size will be extremely subjective unless we can arrive at an objective way to assess group size. Since 1σ, 2 σ, 1D, and 2D are determined by experiment, the size and number of peak-capacity units depend on the user-assigned values of resolutions 1Rs and 2 Rs, which behave like smoothing parameters. For m randomly positioned peaks in a two-dimensional space with first and second dimensions spanned by 1D, and 2D, and rectangular peak-capacity units © 2012 Taylor & Francis Group, LLC

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spanned by 41 σ 1 Rs and 42 σ 2 Rs, the theoretical expression for fcov based on Poisson statistics is [55]



 16 1 σ 2 σ 1 Rs 2 Rs  fcov = 1 − exp  − m  1 2 D D  

(4.14)

Gilar et al. [110] reported another expression for fcov of a random separation, as calculated from the uniform distribution of balls in bins. Panel (c) of Figure 4.18 is a graph of fcov versus the equal resolutions 1Rs = 2 Rs for different m, 1D / 4 1 σ, and 2 D / 4 2 σ values (these are the 1D and 2D peak capacities at unit resolution). As the resolution factors increase, the peak-capacity units become larger in size and fewer in number. The symbols are the average fraction of occupied units in 100 simulations of m random peaks. For a given m, the results are independent of 1D / 4 1 σ and 2D / 4 2 σ, as long as their product (here, 1,250) is constant. The curves are graphs of Equation 4.14 and agree with simulation. It is clear that fcov varies with 1Rs and 2 Rs. Panel (d) of Figure 4.18 is a similar graph using the 598 correlated coordinates in Figure 4.18(a, b) and various combinations 1D 2 D / 16 1 σ 2 σ equaling 500 and 2,000. The same trends are found, although fcov varies slightly with the individual factors, 1D / 4 1 σ and 2D / 4 2 σ, because of correlation. Clearly, fcov is very sensitive to the resolution chosen as the basis for the calculation. One approach to dealing with this is to adopt a specific resolution (e.g., unity) against which all comparisons should be made. However, this action is somewhat arbitrary and needs to be explored. 4.3.3.4  Assessment of Current Metrics for Practical Peak Capacity and Fractional Coverage Our view is that good metrics of practical peak capacity and fractional coverage for two-dimensional separations are currently lacking. The practical peak capacity of Liu et al. only roughly correlates with known areas occupied by peak coordinates (see Figure 4.16). The metrics of Jandera et al. do not appear to apply to solutes lacking repeat units. The method of Davis requires randomly spaced peak coordinates, a rarity in LC × LC. The ecological home range is well researched but its computation requires specialized algorithms. The method of Gilar et al., while intuitive and simple, is sensitive to the resolution (see Section 4.3.3.3). The method of Stoll also is intuitive and simple but lacks rigorous criteria for application. Criteria are well defined for the occupied areas proposed by Ryan et al. and Bedani et al., but such areas can include large, empty regions devoid of peak coordinates. Whether such regions should contribute to the fractional coverage is a matter of debate, even among us. The importance of a good metric for fractional coverage should not be underestimated. Without its accurate assessment, the fraction of the total two-dimensional peak capacity used for separation cannot be evaluated. This makes it difficult to compare two-dimensional separations to each other or to compare a two-dimensional separation to a one-dimensional separation. Even the elegant and sophisticated models for the corrected two-dimensional peak capacity discussed in the next section have a limited use, without some good measure of the fractional coverage. © 2012 Taylor & Francis Group, LLC

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4.4  Optimization in Online LC × LC The subject of optimization in LC × LC has many aspects, and various papers have focused on one or more of the related features [40,49,60,69,111–113]. These include the optimization of the fractional coverage and orthogonality [111], choice of mode combinations [112], mobile phases [69,113], and the design of approaches to implementing optimal second-dimension gradient elution schemes [49,60,111]. Optimization is a common issue in all types of two-dimensional methods, including off-line, stop and go [40], and online LC × LC. Among the various optimization goals is the maximization of the peak capacity in some desired total analysis time or the development of some target peak capacity in the least time. Other goals may also be important, including those related to maximizing the signal by minimizing the overall dilution of the sample [37,114] or optimizing the precision of analysis, especially when using multivariate detectors [21,115]. As pointed out by several groups, optimization in online LC × LC is most severely constrained by the fact that, in the online mode, each time a sample is transferred from the 1D to the 2D, the sample must be injected, the separation run, and the 2D column and system made ready for the next run during the time allotted for the collection of the sample from the 1D column. Thus, one must optimize 1nc and 2 n and the coupling of the two through the undersampling correction factor (, c Equation 4.9) must be taken into account. Horie et al. [41] were the first to quantify some of the key implications of undersampling to the optimization of peak capacity in online LC × LC. Their approach was based on Seeley’s [32] method, discussed in Section 4.2.1, of quantifying the undersampling problem. This work was followed by that of Li, Stoll, and Carr [116] and Potts et al. [117], which pointed out the implications of undersampling on the importance of the first dimension. The basic problem is easily understood through the diagram in Figure 4.19. Here, we show the fact that 2 nc invariably increases monotonically with

Normalized Components of Peak Capacity

1.2 1

b

a

0.8 0.6 0.4

c

0.2

d

0

0

10

20

30 ts (seconds)

40

50

60

Figure 4.19  Plot of normalized contributors to the overall two-dimensional peak capacity. Curve a ( ) is 2 nc normalized to its limiting value at long times; curve b (---) is 1/ according to Davis; curve c (⁃⁃⁃⁃) is the normalized value of 2 nc /; curve d ( ) is the same as curve c but is based on Seeley’s estimate. 1nc = 100; 1tg = 30 min; 1σ = 4.5 s. © 2012 Taylor & Francis Group, LLC

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the second-dimension cycle time, which in online LC × LC is identical to the firstdimension sampling time. The undersampling correction factor (1/) decreases monotonically as the sampling time (ts) increases and thus the resulting normalized overall LC × LC peak capacity first increases, due to the trend in 2 nc, to a maximum and then falls off as 1 dominates. Obviously, the maximum in nc,2D occurs when the rate of increase in 2 nc is exactly equal to the rate of decrease in 1/. Some groups [37] have used the estimate of Seeley [32] and Horie [41], and this makes a definite difference (see curve d in Figure 4.19) to both the peak capacity and sampling time at which the optimum is found. Thus, one of the most fundamental issues in optimizing LC × LC is establishing the optimum sampling rate.

4.4.1  Comparison of Isocratic and Gradient Peak Capacity It is evident that nc,2D must depend on the peak capacities of the two contributing dimensions, so before taking up the details of the optimization of the overall system, we need to be familiar with the chief factors that establish the isocratic and gradient peak capacity. Grushka [118] long ago derived the approximate equation for the isocratic peak capacity nc,iso as defined by Giddings [119]: nc ,iso = 1 +

N  t R ,last  ln 4 Rs  t R , first 

(4.15)

Here, Rs is the resolution factor, which will be taken as unity in all subsequent equations. It is very helpful to keep in mind that with a resolution of unity, the adjacent peak maxima are separated by 4σ units in time. N is the isocratic plate count and the tR values are for the first and last peaks, respectively. The peak capacity in gradient elution nc,grad , assuming a resolution of unity, is computed based on the reasonable assumption that all gradient peaks have approximately the same width (w); thus,



nc ,grad = 1 +

(t R ,last − t R , first ) w

(4.16)

The theory of peak width under linear gradient elution conditions was developed by Poppe assuming that the linear solvent strength equation governs the retention factor [120]:

ln k = ln k w − Sφ

(4.17)



t R = to (1 + (1/ b) ln(b ⋅ ko + 1)

(4.18)

with the dimensionless gradient slope (b) defined as b≡



S∆φto tg

(4.19)

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In the preceding equations, S is the slope of a plot of ln k versus ϕ, where ϕ is the fraction of organic solvent in the mobile phase, to is the column dead time, tg is the gradient time, ko is the solute retention factor when ϕ = ϕo , and k w is the retention factor in a purely aqueous mobile phase. For most practical purposes, the width (at 4σ, i.e., Rs = 1.0) of a given peak will be about w=

4to (1 + ke ) N



(4.20)

This assumes that the gradient compression factor is close to unity; ke is the solute retention factor when the solute arrives at the column exit. Assuming that the gradient elution dwell time is negligible and there is no delay in sample injection relative to the start of the gradient, ke is given by Equation 4.21: ke =

ko 1 + S∆φ

to ko tg

(4.21)

When the second term in the denominator is much larger than 1.0, ke reaches its limiting value, as does the peak capacity: nc ,grad ≈ 1 +

N S∆φ (t R ,last − t R ,1 ) 4 S∆φto + t g

(4.22)

The time of the last peak is taken as tg + to and the time of the first peak is to; thus, the final approximation is

nc ,grad ≈ 1 +

at N S∆φt g ≈ 1g 4 S∆φto + t g a2 + t g

(4.23)

We note that if everything but tg is held constant, at large tg the peak capacity approaches the limit a1. The performances of the same column (3 cm column packed with 1.8 μm particles; assuming a reasonable reduced plate height, we take N = 3,000) under isocratic and gradient conditions are shown in Figure 4.20. If no column reequilibration is required, the gradient system produces more peak capacity than does the isocratic system. If 10 s are required for reequilibration, the isocratic is always superior to the gradient system with SΔ ϕ = 3.3. It is evident that when the reequilibration time is as short as 2 s, the gradient peak capacity at times longer than 2 s but less than 12 s exceeds that of isocratic elution. It is interesting to note that, in Figure 4.20, panel (a), at about 12 s the isocratic peak capacity exceeds the gradient peak capacity. This is due to the asymptotic limiting behavior of Equation 4.23 as compared to Equation 4.15. When the parameter © 2012 Taylor & Francis Group, LLC

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50

Isocratic

40

0

30

1 2

20

3

10 0

169

10 0

10

20

30

Time of Last Peak (sec) (a) 120

Isocratic

Peak Capacity

100

0

80

1

60

2

40

3

20 0

10 0

10 20 Time of Last Peak (sec)

30

(b)

Figure 4.20  Time dependence of isocratic and gradient peak capacity. N is taken as 3,000 for all curves. The gradient time is equated to the time of the last peak less the time needed to reequilibrate (treeq) the column. No reequilibration is needed for isocratic separations. In all cases, to = 1 s, A = 1, B = 1.5, C = 0.1, L = 3 cm, Dm = 10 –5 cm2/s. (a) SΔϕ = 3.3; (b) SΔϕ = 10. Legend gives the reequilibration times.

SΔ ϕ = 10 (see Figure 4.20, panel b), the gradient system is quite superior to the isocratic system except when the reequilibration time is quite long. Evidently, it is thus vitally important to be able to flush the gradient elution pumping system rapidly and reequilibrate the column quickly [121–123]. The fact that the superiority of gradient elution to isocratic elution depends on the sample is evident in the impact of SΔ ϕ in these plots. We neglected the impact of extra-column broadening factors such as injection and transport to the column in the calculations in this figure. These generally have a much larger effect in isocratic than in gradient elution chromatography due to the gradient focusing effect on strongly retained solutes, which can all but eliminate precolumn extra-column effects [114].

4.4.2  Optimization of Peak Capacity in Gradient and Isocratic Elution Chromatography Clearly, the optimization of the overall peak capacity in online LC × LC requires optimization of the individual peak capacity contributions and, as pointed out before, their coupling. Thus, we must review some aspects of optimization of the efficiency and peak capacity in both isocratic and gradient elution chromatography. These topics have been the subject of many reviews (e.g., the magisterial review of Guiochon © 2012 Taylor & Francis Group, LLC

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[124]), so we will be as succinct as possible here. Because the issue of speed is very important, especially in regard to the second dimension, we will follow closely our recent work on fast liquid chromatography [125]. Over the past decade, the Poppe plot [126] and its variants, known as kinetic plots [127,128], have become widely used in isocratic and gradient [129] elution chromatography. In the basic approach of Poppe [126], one chooses the desired particle size, operating pressure, and temperature for a column of a desired set of dynamic characteristics (specifically, the dimensionless A, B, and C parameters of the reduced van Deemter or Knox equations as well as the flow resistance parameter Φ of the Kozeny–Carman equation, typically taken as 500 for a column packed with fully porous particles). One then sets a desired analysis time in terms of the column dead time (to) and varies the column length and velocity until their optimum values (denoted L* and u*e ) that yield the maximum possible plate count (N*) are achieved. It has been shown that this is equivalent to solving the two following simultaneous equations, which restrict the analysis time and pressure [129] for the optimum values of L* and u*e. Once these are known, the plate height and thus the optimum plate count N* for the optimized column length and velocity will be established: L=

εe ueto ε e + ε i (1 − ε e ) P = Φη



(4.24)

ue L d p2

(4.25)

In a Poppe plot, one then plots log (to /N* ) versus log (N* ). A series of such plots for 1.8 μm particles at various maximum pressures and operating temperatures are shown in Figure 4.21. –2.0

a

–2.2 log to/N

–2.4 b

–2.6 –2.8 –3.0 –3.2 –3.4

c 3.0

3.5

4.0

log N

4.5

5.0

5.5

Figure 4.21  Plot of speed (to /N) versus efficiency (N). See text for computation. All plots are done assuming 1.8 μm particles; Dm = 6 × 10 –6 cm2/s (MW = 350, 40°C); εe = 0.38, εi = 0.3, η = 0.0007 Pa s (at 20% ACN/W, 40°C); Φ = 540; A = 1; B = 1.5; C = 0.1; all pressure and plate heights based on ue. N is optimized by the Poppe method for various to with Pmax and T as specified below. Curve (a) 400 bar, 40°C ( ); curve (b) 1200 bar, 40°C (   ); curve (c) 400 bar, 120°C (⁃⁃⁃⁃). © 2012 Taylor & Francis Group, LLC

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a

1.30 1.10 log tR,last/nc,iso

0.90

b

0.70 0.50 0.30 0.10 –0.10 c

–0.30 –0.50

1.2

1.4

1.6

1.8

2.0 log nc,iso

2.2

2.4

2.6

2.8

Figure 4.22  Plot of rate of production of isocratic peak capacity versus peak capacity; all plots are made assuming 1.8 μm particles, isocratic elution, and maximum retention factor of 10; all other factors as in Figure 4.21. Curve (a) 400 bar, 40 °C ( ); curve (b) 1200 bar, 40 °C (   ); curve (c) 400 bar, 120 °C (⁃⁃⁃⁃⁃).

Under isocratic conditions, one can then easily compute the peak capacity (see Equation 4.15), given a maximum desired value of the retention factor for the last peak. This will be the best peak capacity that can be obtained with that size particle, with the limiting pressure and the other conditions chosen for the calculation. The peak capacity plots corresponding to the conventional plate count Poppe plots of Figure 4.21 are plotted in Figure 4.22. Here we chose a maximum retention factor of 10. These curves (see Figure 4.22) have very nearly the same shape and show the same trends versus pressure and temperature as do the plots of plate count (see Figure 4.21). The concept of the gradient peak capacity Poppe plot was introduced by Wang et al. [129], using a more sophisticated approach than used here. Their method took into account the variation in retention of a particular set of solutes based on the individual solute sensitivities to changes in eluent composition. We will simply use Equation 4.23, using a value of tg that corresponds to a gradient retention factor of 10, to generate the gradient peak capacity Poppe plot shown in Figure  4.23. The reequilibration time is taken as 3 s [116,130]. It is most important to understand that gradient elution is much more powerful than is isocratic elution. The two are compared directly in Figure 4.24 (panels a and b). In Figure 4.24(a), we observe the same “crossover” behavior as seen in Figure 4.20(a). This is due to the asymptotic form of Equation 4.23 and the low value of SΔϕ; however, the superiority of gradient elution is clearly evident in Figure 4.24(b). Again, we point out that extra-column broadening is entirely neglected and this will assuredly have a much greater deleterious effect on isocratic versus gradient elution. Based on the superiority of gradient elution, we believe that it is very important that the second dimension (which is by far the more critical dimension in online © 2012 Taylor & Francis Group, LLC

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log tg/nc,grad

1.5 1.0

b

0.5 0.0

–0.5 –1.0

c 1.2

1.4

1.6

1.8

2.0 2.2 log nc,grad

2.4

2.6

2.8

Figure 4.23  Plot of rate of production of gradient peak capacity versus peak capacity; all plots are made assuming 1.8 μm particles, the last retention time is taken as 11to, and the gradient time is equal to the last retention time minus 3 to to correct for column reequilibration. SΔϕ = 3.3; all other conditions as in Figure 4.21. Curve (a) 400 bar, 40 °C ( ); curve (b) 1200 bar, 40 °C (   ); curve (c) 400 bar, 120 °C (⁃⁃⁃⁃⁃⁃). 2.0 b

1.5

a

log tg/nc

1.0 0.5 0.0 –0.5 –1.0

1.2

1.7

log nc

2.2

2.7

(a)

2.0

a

1.5

b

log tg/nc

1.0 0.5 0.0 –0.5 –1.0

1.2

1.7

2.2 log nc

2.7

3.2

(b)

Figure 4.24  Comparison of gradient and isocratic peak capacity. The last peak elutes isocratically and in the gradient at 11 to. No extra-column broadening is assumed in either case. All conditions as given in Figures 4.21–4.23. Panel (a): SΔϕ = 3.3; panel (b): SΔϕ = 10. Pmax = 400 bar; T = 40°C. Curve (a) ( ) isocratic; curve (b) (- - - -) gradient. © 2012 Taylor & Francis Group, LLC

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LC × LC [see the following discussion]) be done by gradient elution if at all possible. This suggests that, if SEC is combined with another mode, the SEC should be implemented in the first dimension. Since reversed phase chromatography is generally more efficient and faster than normal phase and ion exchange chromatography, and reequilibration in reversed phase is reasonably fast, there is considerable impetus for using reversed phase in the second dimension [21].

4.4.3  Early Studies of Optimization in Online LC × LC In this section we will focus primarily on the works of Schoenmakers et al. [130], Horie et al. [41], and Li et al. [116], which were the first studies to consider the optimization of the sampling time issue in online LC × LC. These studies are in many ways closely related, but with substantial differences in detail. 4.4.3.1  Schoenmakers et al. This work [131] appears to be the earliest systematic study of the optimization of online peak capacity in LC × LC. A detailed protocol (algorithm) for choosing all of the operational variables—that is, column lengths, column diameters, particle diameters, flow rates and volumes injected for both the first and second dimension—was described. In addition, optimization of the column temperature was explored. The authors used the method of Poppe [126] described earlier to optimize performance. The important issue of the degree of dilution of the sample was also considered. Unfortunately, a significant limitation of this work was the author’s assumption that to minimize the impact of undersampling, the second-dimension retention time had to be set equal to the first-dimension standard deviation (ts = 2tR,last = 1σ). This sampling rate is actually twice as fast as the sampling rate recommended by Murphy et al. [28] (ts = 2 1σ). While this sampling rate will all but eliminate the undersampling phenomena (see Section 4.2 and Figure 4.19), it will not allow full optimization of the peak capacity. The authors conclude that the attainable peak capacity of LC  ×  LC can be an order of magnitude better than in 1D-LC; their findings regarding the design of optimal systems are summarized as follows. They find that the first dimension should be run using longer columns and much lower velocity than the second dimension and, unless some form of sample focusing in the second dimension can be employed, the second-dimension column will need to be much wider than the first dimension. Monolithic columns, due to their higher permeability, will be useful in the first dimension. Higher pressures will help when implemented in both dimensions. Lastly, LC × LC × LC is likely going to be very impractical due to dilution effects and other practical considerations. These conclusions are more or less all qualitatively correct but quantitatively incorrect. We will not go into this work in detail because it has been largely superseded by a subsequent much more detailed study from a group also led by Schoenmakers [37]. 4.4.3.2  Horie et al. The next major study of the theory of optimization of online LC × LC was that of the Tanaka group [41]. In contrast to the work of Schoenmakers et al. [131], where © 2012 Taylor & Francis Group, LLC

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the sampling time was assumed to be fixed, the chief focus of this work was on finding the optimum sampling time for the first dimension. The authors recognized that the time allowed for the second dimension had to be equal to the 1D sampling time. They assumed that gradient elution would be employed in the first dimension and that isocratic elution would be used in the second dimension so as to avoid the need to reequilibrate the column and flush the instrument. They then computed the 2D isocratic peak capacity as a function of the maximum allowable retention time and the linear velocity of columns of different lengths and particle diameter; monolithic columns were also considered. They did not optimize by working at the maximum allowable pressure drop with the longest possible column as in the Poppe approach. No correction was made for extra-column broadening effects, although their potential impact was described qualitatively. This was then combined with the estimated first-dimension peak capacity and the undersampling correction factor to give plots of nc,2D versus maximum 2D retention time and velocity. The authors recommended that on average about 0.55 samples be taken per first-dimension standard deviation (ts = 2tR,last = 2.2–4 1 σ). This is almost half as fast as recommended by Schoenmakers et al. [131] and about the same as recommended by Murphy et al. [28]. The key results for a reasonable length 2D column are given in Table 4.3. Some of the assumed first-dimension peak capacities are unrealistically high (e.g., 360 units of peak capacity in 1 h). In the range of achievable peak widths, the sampling time ranges from 1.9 to 2.9 in units of 1 σ. Sampling can become slower as the firstdimension peak capacity becomes lower. The monolithic columns are slightly inferior to the 2 μm particle columns but are superior to 5 μm particle columns (results not shown here).

Table 4.3 Optimization Results of Horiea Column Type nc ts in 1σ Maximum nc,2D ts in 1σ Maximum nc,2D 1

2 μm

Monolith

a

First-dimension peak width (seconds) 5 10 30 720 360 120 10.2 5.9 2.9 3800 3250 2190

60 60 2.2 1560

6 3470

1.9 1100

3.7 2760

2.2 1660

A 2.5 cm column is used in both cases and all results correspond to a maximum pressure of less than 40 MPa. A diffusion coefficient of 10–5 cm2/s is assumed. The flow resistance parameter Φ is 1,000 and the viscosity is 0.001 Pa s. The first dimension gradient time is set at 1 h.

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The authors based their undersampling correction on the method developed by Seeley [32] (see Section 4.2). The relationship they used between the undersampling factor and sampling time and thus the second-dimension analysis time was almost identical to that used by Seeley. Thus, in comparison to the method of Davis et al. [36], the Horie work will overestimate the effective first-dimension peak capacity and the overall two-dimensional peak capacity and overestimate the optimum sampling time (see Figure 4.19, curves c and d). They predicted that an undersampling corrected two-dimensional peak capacity of 4,600 could be produced in 1 h in online LC × LC using an isocratic second dimension. This estimate has been revised substantially downward by subsequent work from other groups (see following discussions). 4.4.3.3  Li et al. Although it was not specifically concerned with the problem of optimization of peak capacity, in a study that appeared early in 2009, Li et al. [116] developed some equations that clearly show the fact that there is an optimum sampling time, as shown in Figure 4.19, and that otherwise points out some important interactions between the two dimensions. Combining the Davis undersampling equation (Equation 4.9) with values for the sampling time and an estimate of the first-dimension standard deviation based on the first-dimension peak capacity, t s = 2 tc

1



nc = 1 +

(4.26)

1

t g 1t g t ≅ = 1g w w 4 σ

(4.27)

2



 2t 1n  β = 1 + 3.35  1c c   t g 

(4.28)

gives the final result: nc′,2 D =

1

nc × 2 nc

 2t 1n  1 + 3.35  c1 c   tg 

2



(4.29)

where 2tc is the 2D cycle time. Since it is evident that 2 nc will increase as 2tc increases (see Figures 4.22–4.24), there must be an optimum in a plot of the corrected nc,2D versus 2tc. A series of plots based on Equation 4.29 are given in Figure 4.25. It is evident that the optimum sampling time is longer than that found by Horie et al. [41]. The 1σ value in this figure is 4.5 s (1w = 18 seconds). Thus, we see that the optimum sampling time shifts from about 3.5 to about 4.5 1σ in this case. This is partially due to the use of an empirical relationship (Equation 4.30) between the 2D gradient time and gradient peak © 2012 Taylor & Francis Group, LLC

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Corrected 2D Peak Capacity

1200 1000 800 600 400 200 0

0

10

ts/1σ

20

30

Figure 4.25  Effect of sampling time on the corrected two-dimensional peak capacity (see Equation 4.29). First-dimension peak capacity and gradient time are taken as 100 and 30 min, respectively. The reequilibration times are given in the figure. Curve (a) treeq = 0 s ( ); curve (b) treeq = 3 s (- - -); curve (c) t reeq = 6 s (⁃⁃⁃⁃⁃⁃). 2 n c from Equation 4.30 with nlim = 40 and τ = 25 s.

capacity based on experimental data [116] in comparison to Horie’s use of an isocratic separation in the second dimension:

nc ,2 D = nlim (1 − exp(− 2t g / τ))

(4.30)

with nlim = 40 and τ = 25 s. The figure makes it clear that as the reequilibration time is increased, the optimum sampling time increases and the maximum attainable two-dimensional peak capacity decreases. Figure  4.26 shows the dependence of the peak capacity at fixed 1D time on the 1D peak capacity as a function of sampling time. As the 1D peak capacity increases, the corrected two-dimensional peak capacity increases but not by nearly the same factor as does the first dimension. We also note that ts becomes bigger relative to 1σ; however, it must be understood that, as 1nc is increased at fixed 1tg, it follows that 1w and 1σ must decrease. Thus, the absolute value of ts must also decrease. The impact of the 1D gradient time at fixed 1D peak capacity is very substantial, as shown in Figure 4.27. The maximum corrected two-dimensional peak capacity is almost proportional to 1tg and becomes so under conditions of strong undersampling. The fact that the maxima in Figures 4.26 and 4.27 vary with both the 1D gradient peak capacity and time strongly suggests the complexity of the overall optimization process as the 1D peak capacity will vary with the 1D gradient time. These interactions make the overall optimization quite complex. Also note that the optimum sampling time relative to 1 σ decreases from 7.6 to 3.0 as the gradient time increases from 15 to 60 min. Of course, the actual peak 1 σ value increases with 1t , so the actual t must increase as 1t is increased. As Guiochon has pointed out, g s g the recommended sampling time of Murphy et al. [28] i.e., ts = 21σ “is advice not © 2012 Taylor & Francis Group, LLC

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1000 900 800 700 600 500 400

a

300

c

200

b

100 0

0

10

20

30

40

ts/1σ

Figure 4.26  Plot of corrected two-dimensional peak capacity versus sampling time for different values of the first-dimension peak capacity. The first-dimension retention time is fixed at 30 min and the reequilbration time at 3 s. All other conditions according to Figure 4.25. Curve (a) 1nc = 150 ( ); curve (b) 1nc = 100 (     ); curve (c) 1nc = 50 (⁃⁃⁃⁃⁃⁃).

a commandment.” Clearly the optimum number of samples per peak width varies considerably with the undersampling correction, the rate of production of 2D peak capacity as well as the 1D gradient time and peak capacity. Another issue scarcely as yet treated concerns the impact of the sampling time on peak quantitation. In Section 4.5 we will discuss this to some extent in terms of the optimum number of samples to be taken per peak for accurate and precise integration of the peak. However, there

Corrected 2D Peak Capacity

1600 1400

a

1200 1000

b

800 600

c

400 200 0

0

10

20 ts/1σ

30

40

Figure 4.27  Plot of corrected two-dimensional peak capacity versus sampling time at different values of the first-dimension gradient time at fixed first-dimension peak capacity. The first-dimension peak capacity was fixed at 100 and the reequilibration time was 3 s. All other conditions as in Figure 4.25. Curve (a) 1tg = 60 min ( ); curve (b) 1tg = 30 min (     ); curve (c) 1tg = 15 min (⁃⁃⁃⁃⁃⁃). © 2012 Taylor & Francis Group, LLC

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does not yet appear to be any work on the impact of sampling time when peaks are quantified by using multivariate chemometric methods. The weakened dependence of the corrected peak capacity on 1nc and the strong dependence on 1tg observed in Figures 4.26 and 4.27 are inherent in Equation 4.29. Inspection of Equation 4.29 shows that, as the degree of undersampling increases, the dependence of the corrected two-dimensional peak capacity on the first-dimension peak capacity weakens until, in the limit as undersampling becomes quite severe, the corrected two-dimensional peak capacity becomes independent of the first-dimension peak capacity (see Figure 4.28). 1

nc′,2 D ≅

t g 2 nc

1.83 2tc



(4.31)

Clearly, Equation 4.31 is equivalent to taking the corrected first-dimension peak capacity equal to 1 1



nc′, ≅

tg

1.83 2tc

=

f 1.83

(4.32)

Corrected Second Dimension Peak Capacity

where f is the number of fractions taken from the first dimension ( f = 1tg / 2tc ). The fact that the corrected peak capacity becomes independent of the 1D peak capacity clearly implies that the first dimension need not be precisely optimized to get very good overall two-dimensional peak capacities. This result from Li’s study 2500 a

2000 1500 b

1000

c

500 0

0

100 200 300 First Dimension Peak Capacity

400

Figure 4.28  Plot of corrected two-dimensional peak capacity versus first-dimension peak capacity at different first-dimension gradient times. The second-dimension cycle time (= ts) was fixed at 21 s. The second-dimension gradient time was 18 s and the reequilibration time was 3 s. All other conditions as in Figure 4.27. The approximate number of fractions taken from the first dimension are also given. Curve (a) 1tg = 60 min ( ), 172 fractions taken; curve (b) 1tg = 30 min (     ), 86 fractions taken; curve (c) 1tg = 15 min (⁃⁃⁃⁃⁃⁃), 43 fractions taken. © 2012 Taylor & Francis Group, LLC

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Table 4.4 Estimated Limiting Two-Dimensional Corrected Peak Capacitya 2

First-Dimension Gradient Time (min) 5 15 30 60 90 120 240 a

nc  / 2tc (peaks/second) 0.5

1.0

2.0

82 246 492 984 1,476 1,968 3,860

164 492 984 1,968 2,952 3,936 7,872

328 984 1,968 3,936 5,904 7,872 15,744

Based on Equation 4.31.

was subsequently confirmed in greater detail in various papers from the Guiochon group [38,40] as well as from Potts et al. [117]. This restriction does not apply to off-line work; however, the price paid for this freedom is that off-line LC × LC generally takes a lot more time to carry out than online LC × LC. It is clear that as one allows more time, the peak capacity will increase continuously. Some limiting values of the peak capacity computed from Equation 4.31 assuming different values for 2 nc / 2tc are given in Table 4.4. Potts et al. derived an equation for estimating the 1D peak capacity that produces 90% of the limiting value of the corrected twodimensional peak capacity: 1



1 t nc ,0.9 ≥ 1.13 2 g tc

(4.33)

Clearly, longer 1D gradients and faster 2D gradients yield greater 1D peak capacities. Some results are given in Table 4.5.

4.4.4  More Recent Detailed Studies of Optimization 4.4.4.1  Guiochon Group Beginning in 2009, Guiochon and his co-workers published a very important series of papers that treat many of the details in the optimization of both online and off-line LC × LC as well as separation with multiple parallel 2D columns and issues related to detection [38–40,90,114,132]. At this point we will focus attention on his work centered on online LC × LC, which is the central theme of this chapter. Very early in the paper, this group makes the perceptive comment that “it is impossible to develop an online 2D-LC separation that is fast and at the same time has a high peak capacity.” © 2012 Taylor & Francis Group, LLC

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Table 4.5 Limiting First-Dimension Peak Capacitya Second-Dimension Cycle Time (s) First-Dimension Gradient Time (min) 5 15 30 60 90 120 240 a

10

20

40

60

34 102 203 407 610 814 1627

17 51 102 203 305 407 814

9 25 51 102 153 203 407

6 17 34 68 102 136 271

Based on Equation 4.33.

Clearly, there are limits to both speed and peak capacity in online LC × LC, which is the principal focus of their contribution. In many ways, the Guiochon group took a rather different approach to the optimization problem from any of the work that preceded it, although it was very much built on the prior efforts of others. Their key equation for the computation of the corrected two-dimensional peak capacity (n′c,2D) is derived in the appendix at the end of this chapter.

nc′,2 D =

λ 1t g 2

w r 2 + 3.35



(4.34)

To develop this equation Guiochon introduced two new terms: r and λ. The first is simply the number of samples taken across each first-dimension peak and the second denotes the fraction of the each second-dimension cycle, which is devoted to running the second-dimension gradient: r≡



1

w 1w = 2 ts tc

2 2 t t − 2t λ ≡ 2 g = c 2 reeq    with 0 < λ < 1 tc tc

(4.35)

(4.36)

As Guiochon said, the real separating power of two-dimensional chromatography comes from the fact that the timescale of the whole measurement (1tg) is independent of the second-dimension peak width; that is, 2w does not increase as 1tg is increased, whereas 1w must. Guiochon points out that, based on Equation 4.34, there © 2012 Taylor & Francis Group, LLC

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are only three things that can be done to maximize the corrected two-dimensional peak capacity: • One can make the first-dimension gradient time as long as possible. Of course, this means that the overall analysis time will be large. • One can maximize λ. This means that the 2D column reequilibration and other factors that add to 2tg to establish 2tc must be minimized. • The denominator in Equation 4.34 must be minimized. It is important to understand that 2w and r are strongly coupled and cannot be independently varied. In fact, the main focus of this paper is in understanding the factors that control 2w. Making the usual assumptions about gradient system dwell time and employing Equation 4.18 for the gradient retention time, Guiochon developed an equation for 2w for the last peak eluting from the column. An equation for the peak width that corrects for the compression of the rear edge of the peak [120,133]) was also used. Because this greatly complicates the algebra and is ignored by almost everyone else, we will continue to use Equation 4.20. Assuming that the retention factor (ko) at the initial eluent composition (ϕo) is much greater than 1/b, as does Guiochon, we can approximate the second-dimension peak width as 2



w≈

4 2to ( 2 b + 1) 2 b 2N

(4.37)

Clearly, the second-dimension peak width varies with the dimensionless gradient slope (2 b). Starting at values of 2 b less than 1.0 corresponding to large values of 2 tg, and small values of 2 to, S, and Δϕ, the peak width will decrease as 2 b is increased until, under very fast gradients, the peak width becomes independent of 2 b. Guiochon points out that the values of the second dimensionless gradient slope (2 b) must be equal to those that make the last peak elute at 2 tg. Thus, he solves Equation 4.18 for the value of 2 b that makes 2 tR,last equal to 2 tg. A plot of b versus 2 tg/2 to for values of k o in the range considered by Guiochon is given in Figure 4.29. In essence, all of the variables (S, to, tg, Δϕ) that control b except Δϕ are known (see Equation 4.19). Thus, once b is established, one can back-calculate Δϕ and, given the initial eluent composition, one can then compute the final eluent composition needed to make the last peak elute at 2tg. Of course, only b values that correspond to Δϕ < 1 make physical sense and Guiochon limits his calculation to this range. In our view, there is a very small error here. If the numerator of Equation 4.16 is taken as tg, since the first peak cannot elute before to, then the last peak must elute at tg + to, not at tg. Recognizing the need for some minimum time to implement column reequilibration [121–123], the authors correctly add 2 2to to 2tg to get the second-dimension cycle time. Although not explicitly stated in the paper, it appears from the large value of S (43) and small value of Dm (1.7 × 10 –6 cm2/s), chosen for their typical solute, that the quantitative results of the paper apply to peptide-like solutes. © 2012 Taylor & Francis Group, LLC

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1.0

c

b 2.0

a

1.0 0.0

0.6

b

0.4 0.2

d 3

5

φfinal

0.8

3.0

7

9

11 13 tg/to

15

17

19

0.0

Figure 4.29  Value of the dimensionless gradient slope (b) and corresponding final eluent composition (ϕfinal) needed to make the last peak elute at the second-dimension gradient time. Based on the solution of Equation 4.18. Curve (a) b with ko = 100,000 ( ); curve (b) b with ko = 10,000 (- - -); curve (c) ϕfinal with ko = 100,000 (⁃⁃⁃⁃⁃⁃); curve (d) ϕfinal with ko = 10,000 ( ).

The 1D peak capacity was handled much more conventionally. When the dependence of 1nc on 1tg was needed, they used an equation obtained from their experimental work (see Equation 4.38). It should be carefully noted that an equation of this form means that a fixed value of the plate count and thus column length, particle size, and velocity are assumed (see Equation 4.23). It appears that a rather short 1D column was assumed for all calculations. This is a bit surprising since they considered firstdimension gradient times as long as 2 h. It is clear from the experimental work of Stoll et al. [29], Huang et al. [134], and Wang et al. [135,136], as well as the theoretical work of Wang et al. [129] on Poppe optimization of gradient elution, that, as the firstdimension gradient time is increased over a wide range, the column length should be increased and the eluent velocity decreased to maximize the peak capacity: 1



nc =

1751t g 7.5(min) + 1t g



(4.38)

It should be pointed out that just as in the work of Horie et al. [41], Li et al. [116], and Potts et al. [117], the authors did not do true multivariable optimizations because, generally speaking, only one or sometimes two variables at a time were changed. The Poppe method of maximizing N was definitely not used in this work as it was in the work of Schoenmakers and co-workers [37]. Because the undersampling correction and the form of Equation 4.34 are the same as Equation 4.29 used by Li and Potts, many of the results are similar. In particular, the limiting dependence of the corrected two-dimensional peak capacity on 1n seen in Figure 4.28 was also observed. In contrast to Li and Potts, the authors had c the insight to analyze their results in terms of the total number of fractions (f) taken from the first-dimension separation: 1



f=

t g 1t g = 2 ts tc

(4.39)

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Corrected 2D Peak Capacity

1500 1200 900 600 300 0

0

50

100 150 200 250 Number of Collected Fractions ( f )

300

Figure 4.30  Effect of number of fractions (  f  ) and column length on the corrected twodimensional peak capacity. The parameters used for the calculation are 1tg = 2 h, 2uo = 60 cm/min, 2 d = 5 μm, D = 1.66 × 10 –6 cm 2/s, S = 43, k = 105, ϕ = 0.05, 2 L = 3 (- . -), 5 (- - -), 10 (⁃⁃⁃⁃⁃⁃), p m w 0 and 15 cm ( ). (Reprinted with permission from Horvath, K., Fairchild, J. N., and Guiochon, G. 2009. Analytical Chemistry 81:3879–3888, ©American Chemical Society.)

A plot of the corrected two-dimensional peak capacity versus f is shown in Figure 4.30. Guiochon pointed out that as the uncorrected peak capacity of the first dimension begins to exceed the number of fractions taken from the first dimension, the corrected two-dimensional peak capacity is just about at its limiting value and becomes rather independent of any further decrease in 1w at fixed 1tg. Equation 4.33 can be easily recast in terms of f: 1



nc,0.9 ≥ 1.13 f

(4.40)

However, it appears that these authors found that the maximum achievable corrected two-dimensional peak capacity was somewhat lower than the curves produced by Li and by Potts. This is surprising in that virtually the same undersampling correction factor was applied to similar ranges in 1nc values. Indeed, the results of Li and of Potts are based on experimentally measured values of 2 n , whereas Guiochon’s are theoretically computed values. It appears to us that c the value of the C term (0.3) in the van Deemter equation used in this work is extraordinarily conservative. We estimate from the values of A, B, and C given in the paper that h min is about 5.1, which strikes us as very conservative. Finally, Guiochon assumed the use of 5 μm particles, whereas in Li’s work 3 μm particles were employed. All of these differences will lead to lower estimates of the peak capacities. The importance of the 2D column length and velocity are clearly shown in Figures 4.30 and 4.31. The maximum possible peak capacity increases as the seconddimension column is shortened. It is interesting that there is a maximum in each curve versus the number of fractions taken from the first dimension. © 2012 Taylor & Francis Group, LLC

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Corrected 2D Peak Capacity

1500 1200 900 600 300 0

0

2

4

6 8 10 Column Length (cm)

12

14

Figure 4.31  Corrected two-dimensional peak capacity of an online system as a function of the length of the second-dimension column at different eluent velocities. 2 uo = 15 ( ); 30 (⁃⁃⁃⁃); 60 (- - -); 90 cm/min (- . -). All other conditions are as in Figure 4.30. (Reprinted with permission from Horvath, K. et al. 2009. Analytical Chemistry 81:3879–3888, ©American Chemical Society.)

This is, however, easily explained. Because the first-dimension gradient time is fixed and consequently the first-dimension peak capacity is as well, as one varies f, the value or 2tc must vary. Thus, this plot is really very analogous to a plot of n′c,2D versus ts such as shown in Figures 4.25–4.27, and consequently, the maximum reflects the compromise between undersampling and the impact of second-dimension gradient time on second-dimension peak capacity. Figure  4.31 shows that at each second-dimension velocity, there is an optimum length. When all other parameters are held constant, the same maximum corrected peak capacity (about 1,200) can be achieved by various combinations of 2 L and 2uo. Guiochon points out that the fall-off at higher column lengths at a fixed 2uo is due to the increase in 2to and thus a decrease in λ (see Equation 4.36). It should be kept in mind that the dimensionless gradient slope is varied at each point in both Figures  4.30 and 4.31 to assure that the last peak does elute at 2tg. The results of Figure 4.31 certainly indicate that there will be an optimum seconddimension column length along with the need to optimize simultaneously both the column length and velocity as Guiochon pointed out. One of the unique contributions of this study is shown in Figure 4.32. The maximum achievable corrected peak capacity is shown as a function of the initial mobile phase composition. The decrease in n′c,2D with increasing ϕo can be explained by the concomitant need to decrease ϕfinal to assure that the last peak elutes at 2tg. The decrease in Δϕ will decrease 2 b and thus increase 2w (see Equation 4.37), thereby decreasing the corrected peak capacity. One of the most important contributions of this paper—one that seems to be quite original with this work—is shown in Figure 4.33. Here the corrected two-dimensional peak capacity is shown as a function of the first-dimension gradient time. This result should not be mistaken for that of Figure 4.28 or the results in Table 4.4 or 4.5. The origin of the limit is evident in Equations 4.34 and 4.38. If we assume that r 2 is much larger than 3.35—that is, there are many samples taken across the © 2012 Taylor & Francis Group, LLC

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1400 1200 1000 800 0

2 4 6 8 10 12 Initial Organic Content of the Eluent (%)

14

Figure 4.32  Corrected two-dimensional peak capacity of an online system as a function of the initial organic content of the eluent in the second dimension. The other parameters are found in Figures 4.29 and 4.30. (Reprinted with permission from Horvath, K. et al. 2009. Analytical Chemistry 81:3879–3888, ©American Chemical Society.)

first-dimension peak width (1w) so that undersampling is unimportant and thus there is no loss in peak capacity—we arrive at

nc′,2 D =

λ 1t g 2

w r2

=

λ 1t g 2 wr

(4.41)

We now replace r with its equivalent using Equation 4.35 and then substitute 1tg / 1nc for 1w: nc′,2 D =



λ 1t g 2tc λ 2tc 1nc = 2 2 1 w w w

(4.42)

Corrected 2D Peak Capacity

5000 4000 3000 2000 1000 0

0

100 200 300 400 First Dimension Analysis Time (min)

500

Figure 4.33  Achievable online corrected LC × LC peak capacity as a function of the firstdimension analysis time. The particle diameter of the stationary phase of the column used in the second dimension is 1.7 μm, the initial organic content of the eluent is 1%, the linear velocity of the eluent is 60 cm/min, and the number of collected fractions is 3 fractions/min, multiplied by 1t . The other parameters are in Figures 4.30–4.32. (Reprinted with permission from Horvath, g K. et al. 2009. Analytical Chemistry 81:3879–3888, ©American Chemical Society. © 2012 Taylor & Francis Group, LLC

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As the first-dimension gradient time becomes larger and larger (everything else remaining constant [see Equation 4.23]), 1nc naturally approaches its limit (here denoted 1nc∞ at large 1tg (see Equation 4.38). Equation 4.42 can be simplified a bit by replacing 2w with 2tg / 2 nc and recalling the definition of λ (see Equation 4.36): nc′,2,∞D =

λ 2tc 1nc∞ 1 ∞ 2 = nc ⋅ nc = 2 w

N S∆φ 2 nc 4

(4.43)

It must be understood that this final equation is an approximation that only works under conditions of minimal undersampling. The fact that Equation 4.43 shows a dependence on N clearly underscores the assumption underpinning Figure 4.33—namely, that the column length and all other conditions that control the plate count are fixed. We point out that if one were to reoptimize the system performance continually as the first-dimension gradient time was increased, the corrected two-dimensional peak capacity would continue to increase and not show the limiting behavior as in Figure 4.33. The results of Guiochon et al. suggest that the maximum possible peak capacity that can be obtained in online LC  ×  LC for peptide-like solutes, which typically give easily twice the peak capacity of small solutes, given almost an indefinitely long analysis time, will not exceed about 4,000. Given the various limitations on the calculations, the authors conclude that online LC × LC “will probably never permit the achievement of peak capacities in excess of 10,000.” 4.4.4.2  Schoenmakers Group The group headed by Schoenmakers has made a number of important contributions to optimization in LC × LC, including several papers related to the best metric of resolution [137,138] and papers on optimization of off-line separations [8,9,139]. Their most recent work directly relevant to this review is a very comprehensive paper on online LC × LC [37]. This paper is, in fact, a true optimization paper in which a detailed algorithm for the simultaneous optimization of particle sizes, column diameters, column lengths, and the eluent velocity in both dimensions as well as optimum sampling time were considered. The column length and velocity were always chosen so as to hold the pressure at Pmax and maximize N. Additionally, the use of both isocratic and gradient elution and their various combinations in both dimensions, as well as the performance of HPLC (40 MPa) and UPLC (100 MPa), was considered. Three goals were defined: maximization of peak capacity, minimization of analysis time, and minimization of total sample dilution in the LC × LC separation process. The Pareto method of multiobjective optimization was employed to define the best compromise in arriving at the overall objective. A major difference between the approach of this work and, for example, that of Guiochon [38] or Horie et al. [41] is that Schoenmakers et al. incorporated the undersampling effect as a detector broadening factor following the ideas of Blumberg [33].

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Thus, the first-dimension peak capacity is computed from an estimate of the peak σ (in time units) corrected for the impact of a slow detector:

1

σ total = ( 1 σ peak )2 +



(ts )2 2 δ det

(4.44)

In this work, δ 2det was taken as 4.76 in accord with Davis’s estimate of the broadening effect [36]. Another important difference in this work from many others, excepting a study of Horvath et al. [114], is the explicit inclusion of the impact of sample injection on the second-dimension peak width. Again, in time units, the volume of the injected sample (=1Fts ) can be accommodated as 2

1



σ total

 1Ft  1 = ( σ) +  2 s  2  F  δ inj 2

2

(4.45)

For a perfect plug injection δ2inj is taken as 12, but experimentally it is better approximated as 4. Equation 4.45 does not account for any sample focusing that might take place if gradient elution were used in the second dimension. Focusing can be a very substantial effect, especially if the sample is injected in a weak solvent when the initial eluent is also very weak so that the sample is virtually trapped at the inlet of the column. The volume injected into the second-dimension column is effectively contracted by the factor (2 k1e + 1)/(2 k2e + 1), where the terms in parentheses are the retention factors of the analyte in the 1D and 2D eluents, respectively [49,140]. The resulting corrected standard deviation is 2

2



2

 1Ft   2 k + 1  1 σ total = ( 2 σ )2 +  2 s   2 2e  2  F   k1e + 1  δ inj

(4.46)

Given Equations 4.44 and 4.46, new equations for the isocratic and gradient peak capacity are derived under the assumption that the extra-column effects are small perturbations on the peak width. The modified peak capacity equations are then used to compute both the 1D and 2D peak capacities as part of the optimization scheme. Another major point of departure of the Schoenmakers group from most others (excepting Horvath et al. [114]) is the explicit consideration of sample dilution as a result of the LC × LC process. One of the important limitations of online LC × LC versus 1D-LC is the double dilution of the sample. This makes detection of lowconcentration species more difficult. Indeed, the fact is that if each first-dimension peak is sampled only two times then, on average, even ignoring dilution, the amount that has to be detected in online LC × LC is 50% of what needs to be detected in 1D-LC. The problem is not as severe in off-line LC × LC because the sample collected from the first-dimension column can be concentrated by various means

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before injection on the second dimension. The overall dilution factor experienced in LC × LC is

DF2 D = 2π

1

σ 2 σ total 2 F 1 Vinj ts

(4.47)

Although it is tempting to compare the results of the Guiochon group quantitatively to those of the Schoenmakers groups, there are just too many details that make the comparison difficult. For example, the A, B, and C van Deemter coefficients are different. More fundamentally, Guiochon uses the interstitial linear velocity (ue), which is undoubtedly the more fundamental term, whereas Schoenmakers uses the more easily measured eluent velocity (um). Guiochon assumes a peptide-like solute, whereas Schoenmakers uses a diffusion coefficient of a low molecular weight solute of 10 –5 cm2/s—nearly 10 times as large as that used by Guiochon. Thus, we will limit ourselves to discussing only some general trends. One of the most important trends is the impact of the number of fractions taken per first-dimension peak (r). Schoenmakers suggests that this should be about two to three. Inspection of Figure  4.34 shows about a 25% loss in the corrected 1

/2Dnc

0.8 0.6 0.4 0.2 0

0

5

10 15 Number of Cuts per Peak

20

Figure 4.34  Fraction of the corrected peak capacity that is actually realized as a function of the number of second-dimension runs per 1D peak. The solid line with “+” symbols includes only band broadening due to undersampling in the first dimension assuming δ2det = 12 whereas the solid curve without “+” symbols assumes δ2det = 4.76. The dashed line includes band broadening due to first-dimension undersampling and second-dimension injection broadening. For the dashed line, a variety of situations have been averaged (e.g., different flow rates, particle sizes, analysis times, etc.). The bars represent the standard deviation of these averages. Conditions of calculations: van Deemter A, B, and C = 1.5, 1, and 0.15, respectively; D m = 10 –5 cm 2/s; Pmax = 40 MPa; column resistance parameter (Φ) = 1,000; dc = 1, 2.5, 5, 7.5, 10 mm; viscosity = 0.001 Pa s; dp = 1.5, 2, 2.5, 3, 3.5, and 4 μm; 1tR,last = 50–200 min; 2 tR,last = 0.1 to 1 min; 1Vinj = 3 μL; SΔϕ = 3.3; tg/tm = 10. (Reprinted with permission from Vivó-Truyols, G. et al. 2010. Analytical Chemistry 82:8525–8536, ©American Chemical Society.) © 2012 Taylor & Francis Group, LLC

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Analysis Time, Min

200

150

100

50

0

2000

4000

2Dn

6000

8000

10000

Figure 4.35  Pareto optimized time and corrected peak capacity for online LC × LC system assuming gradient elution in both dimensions. The solid line represents the total peak capacity without any external band broadening. The dashed line represents the total peak capacity considering only detection band broadening in the first dimension. The dasheddotted line represents the total peak capacity considering detection band broadening in the first dimension and injection band broadening in the second. For all computations, column diameters were fixed at 4 mm. Pmax was taken as 40 MPa. Other conditions as in Figure 4.34. (Reprinted with permission from Vivó-Truyols, G. et al. 2010. Analytical Chemistry 82:8525–8536, ©American Chemical Society.)

two-dimensional peak capacity due only to undersampling (see solid curve without “+” signs). The average loss due to both undersampling and injection volume is much greater (see the dashed curve and open squares), amounting to almost a 75% loss in peak capacity. It is not clear whether significant focusing is allowed to take place, but we would assume not because this amounts to a very drastic loss in performance and underscores the need for focusing in the second dimension. It should be noted that in this figure the Pareto method was not used. The various conditions were averaged together to get the dashed curve and thus the results are far from optimum. In the next part of this study, this group used the Pareto optimality condition to choose those experimental conditions (e.g., particle sizes, analysis times, etc.) that maximize the corrected peak capacity and minimize analysis time (see Figure 4.35). The comparison of the results including the two extra-column broadening factors makes it very clear that the corrected peak capacity is severely limited by both extracolumn broadening factors, even under highly optimized conditions. Under the three conditions, approximately 8,600, 5,000, and 2,100 units of peak capacity can be generated in 200 min. Given that the lowest figure includes both broadening factors, it probably is the most realistic and experimentally accessible one. The figure of 5,000 conceptually is closest to the conditions described in Section 4.4.4.1 from the Guiochon group. At a time of about 200 min, Guiochon predicts about 3,000 units of peak capacity for a peptide-like species; thus, his results are really considerably lower than Schoenmakers’. However, Schoenmakers’ results strike us as fairly low overall, as Stoll et al. [29] have reported experimentally © 2012 Taylor & Francis Group, LLC

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200

Iso × Iso Grd × Iso

UPLC × HPLC Iso × Grd

HPLC × UPLC

Analysis Time, Min

Grd × Grd

150

100 UPLC × UPLC

50

2000

4000

nc,2D

6000

8000

Figure 4.36  Pareto optimized time and corrected peak capacity for online LC × LC system comparing isocratic and gradient separations and the effect of pressure. All separations involving UPLC are made at 100 MPa and in the gradient mode. All other separations are made at 40 MPa. Other conditions as in Figure 4.34. (Reprinted with permission from Vivó-Truyols, G. et al. 2010. Analytical Chemistry 82:8525–8536, ©American Chemical Society.)

measured corrected peak capacities of over 1,000 in 30 min using particles that were no smaller than 3 μm. Nonetheless, it is obvious that the undersampling and injection problems are very real. In Pareto results not shown here, it is very clear that two to three cuts per first-dimension peak width (= 4 1σ) are optimum under a fairly wide range of conditions, in agreement with the Guiochon group. One of the most interesting studies in this paper (see Figure 4.36) made it clear that use of dual gradient LC × LC is very definitely quite superior to dual isocratic LC × LC and both permutations of isocratic and gradient elution chromatography. Furthermore, use of UPLC (100 MPa) in either dimension—and especially in both dimensions—brings about a significant improvement. The fact that use of UPLC only in the second dimension is superior to the use of only UPLC in the first dimension indicates the importance of the second dimension. Inspection of Equation 4.45 shows that as the second-dimension flow rate (2F) is increased, extra-column broadening from injection onto the second-dimension column will be diminished. This can be done at constant linear velocity, thereby holding the inherent peak width constant by simultaneously increasing the 2D column diameter. This strategy is certainly valid, but at the cost of increased total dilution of the sample, as Equation 4.47 makes clear that the two-dimensional dilution factor (DF2D) is proportional to 2F. For this reason, the minimization of dilution was also included as an objective of the Pareto optimization along with maximization of peak © 2012 Taylor & Francis Group, LLC

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10

40 20 0 300

Ana

4000

200

lysis

Tim e,

2000

100

0

Min

0

Analysis Time, Min

Total Dilution

60 150

20 40

100 10

D

n c,2

50 1000

7.5 2000

(a)

3000 4000 nc,2D

5000

6000

200 Analysis Time, Min

Analysis Time, Min

30

(b)

200

150 20 40

100

50

20

7.5

10

200

400 nc,2D

(c)

600

40

150 10

100

50 1000

2000

3000 4000 nc,2D

5000

6000

(d)

Figure 4.37  (a) Pareto optimization resulting from optimizing total 2D corrected peak capacity, total analysis time, and total dilution for an LC × LC system, using the parameters given in previous figures. Gradient elution was used in both dimensions. Overlaid dots represent actual Pareto experiments, whereas the surface represents the linear interpolation of the dots. Panel (b) depicts the iso-dilution map corresponding to panel (a) (the iso-dilution lines at dilution factors of 7.5, 10, or 20 are interpolated, whereas iso-dilution lines at 30 and 40 correspond to actual Pareto experiments). Panels (c) and (d) represent the iso-dilution maps as in panel (b), 2 k +1 but considering different values of 2 2 e . Panel (c) corresponds to a ratio of 2 and panel k1e +1 (d) corresponds to a ratio of 5. The iso-dilution lines in (c) and (d) are not interpolated but rather represent actual computations. (Reprinted with permission from Vivó-Truyols, G. et al. 2010. Analytical Chemistry 82:8525–8536, ©American Chemical Society.)

capacity and minimization of analysis time. The results are given in Figure  4.37, which represents an actual optimization surface. Panel (a) shows that when DF2D is large (e.g., greater than 20), it is a very steep function of both the analysis time and peak capacity and thus minor changes in factors that scarcely change analysis time or peak capacity can greatly reduce dilution and improve peak size. It should be noted that for the results in panels (a) and (b), it was assumed that there was no focusing (that is i.e., 2 k1e and 2 k2e are equal; see Equation 4.47). The numbers on the contour lines are the dilution factors. The fact that the space between the contours is so small shows how steep the plot in panel (a) © 2012 Taylor & Francis Group, LLC

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is. The effect of focusing is shown in panels (c) and (d). The contours become much closer together, indicating that almost no peak capacity or analysis time needs to be sacrificed to reduce the dilution factor greatly. With a focusing factor of five, one can easily lower overall dilution to less than 10. 4.4.4.3  Impact of Multiple Parallel Second-Dimension Columns The Guiochon group has considered in detail the impact of using parallel seconddimension columns [90]. There have been a number of experimental papers in which from two to four columns were used in parallel as the second dimension [141–149]. Generally, the two columns operating in parallel are made to be as similar as possible but Tanaka’s group [146] has investigated the use of parallel columns having quite different selectivity. Here, we will focus exclusively on matched columns. When parallel columns are used in the second dimension, one can attempt to increase the total corrected two-dimensional peak capacity by holding the sampling time constant, or one can decrease the sampling time in proportion to the number of parallel columns. In the latter case, the corrected peak capacity will be approximately constant but the total two-dimensional analysis time will be cut by a factor nearly equivalent to the number of parallel columns used. For simplicity, consider the case of two parallel columns, each of which has the same cycle time (2tc,2, in which the subscript 2 denotes that two columns are used in parallel) and thus the same peak capacity (2nc(2tc,2)). The effluent from the first column is switched into the second column and the second column gradient begun at a time of exactly 2tc,2/2. The sample is switched back to the first column at a time precisely equal to 2tc,2/2. Clearly, the sampling time (ts,2) is 2tc,2/2. Holding the sampling time fixed whether we run two columns or only a single column, it is obvious that 2tc,2 must be equal to twice 2tc,1. Given that 2nc is a monotonically increasing function of the gradient time (see Equation 4.23) and hence the cycle time, the total two-dimensional peak capacity will be greater with two parallel columns than with a single column. Fairchild et al. [90] demonstrated this quantitatively. The results of varying the cycle time with one, two, or three parallel columns are shown in Figure 4.38. It is evident that as the number of columns increases, the maximum achievable two-dimensional peak capacity increases but not quite in proportion to the number of columns. There is also another important result: The optimum second-dimension cycle time also increases from about 16 s with one column to 32 s with three columns, thereby making it easier (experimentally) to attain this better peak capacity. Guiochon pointed out that the gains provided by using two columns are substantial, but that the additional effort required for implementation of three columns, especially hardware costs, become prohibitive for the diminished potential gain. One of the usual objections to using multiple columns is the difficulty in matching columns, but the Guiochon group was sanguine on that point. Another major point of this paper was the fact that one could significantly decrease the overall analysis time by using parallel columns. To show this, one must assume some relationship between the first-dimension peak capacity and the corresponding gradient time. We will adopt the same equation used by Guiochon et al. To produce the plot shown in Figure 4.39, we assume an experimental relationship (Equation 4.48) between the second-dimension peak capacity and the second-dimension gradient time. © 2012 Taylor & Francis Group, LLC

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Corrected 2D Peak Capacity

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c

500

a

0

b

0

20 40 60 80 Second Dimension Cycle Time (s)

100

Figure 4.38  Effect of number of parallel columns on the dependence of the corrected two-dimensional peak capacity on the second-dimension cycle time. All curves generated assuming 1nc = 100, 1tg = 30 min, and using Equation 4.30 for the 2 nc with nlim = 40 and τ = 25 s, ts = 2tc /m, where m is the number of columns. Curve (a) ( ), one column; curve (b) (- - -), two columns; curve (c) (⁃⁃⁃⁃⁃⁃), three columns.

1



nc =

70 ⋅ 1t g 30 min + 1t g



(4.48)

The 2D peak capacity was computed from Equation 4.30 with 2tc = 60 s and treeq = 3 s. It should be pointed out that Guiochon used a quite different method of computing the second-dimension peak capacity but, qualitatively, the same result is obtained: Upon going from one 2D column to two, there is a considerable change in analysis time and a smaller change is seen upon going to three columns. The largest effect of the number of parallel columns will be seen when undersampling is most severe and when the second-dimension peak capacity still depends strongly on 2tc:

Corrected 2D Peak Capacity

2500

c b a

2000 1500 1000 500 0

0

50 100 150 Aggregate Analysis Time (min)

200

Figure 4.39  Plot of corrected two-dimensional peak capacity versus aggregate analysis time and effect of number of parallel columns. All other conditions as in Figure 4.38. Curve (a) ( ), one column; curve (b) (- - -), two columns; curve (c) (⁃⁃⁃⁃⁃⁃), three columns. © 2012 Taylor & Francis Group, LLC

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4.4.5  Summary It is clear from the differences in results in the various papers surveyed here that much remains to be done in working out a systematic approach to optimization in online LC × LC. However, there are areas in which the agreement is good: • There is very little question that from the perspective of optimizing resolution that the M–S–F rule is too conservative and that, in most instances, a sampling rate on the order of ts = 3–4 1 σ, not 2 1 σ , will produce the best resolution for a separation taking about 1 h. As the 1D time is increased, the sampling rate can be made a bit slower. • The second dimension is best operated using small particles, short columns at high velocity at the highest possible pressure and highest possible temperature. The column length and velocity must be optimized to reach the best compromise between the highest 2D peak capacity and least . The second dimension is the critical dimension and should be thoroughly optimized. Undoubtedly, the second dimension will be run at substantially higher flow rate than the first dimension. This entails substantial sample dilution, which can be mitigated by proper optimization of the 1D and 2D column diameters and trade-offs in the respective flow rates. • The first dimension is not as important as the second. The sampling rate will almost certainly be such that there is a significant degree of undersampling and consequently the first dimension does not need to be as thoroughly optimized as the second. This does not mean that one should be profligate with its peak capacity, and the first dimension should not be seriously underpowered deliberately. However, use of long monolithic columns or columns packed with ultrasmall particles (especially if the first-dimension gradient time is on the scale of hours or longer) is not necessary. Indeed, it is very likely that larger particles (perhaps even 5 μ particles) will produce more plates and thus higher peak capacities than 1.8 μ particles, given gradient times of 60 min. • Given conditions of substantial undersampling, increases in the 1D gradient time will increase the corrected LC × LC peak capacity. However, there may be an effective limit in the maximum possible value. There certainly is such a limit if one uses a one-dimensional column of fixed length and operates it at a fixed velocity; however, if one updates the particle size, column length, and velocity as the gradient time is increased, this may not be so. • Gradient elution improves the peak capacity of both dimensions, but it is extremely important that the system flush-out and column reequilibration times be absolutely minimized in the second dimension. • Parallel second-dimension systems are very helpful. They can increase the corrected two-dimensional peak capacity and decrease analysis time needed to generate a specified peak capacity. It is doubtful that the gain in using more than three systems would be worth the additional cost and maintenance.

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4.5  Quantification Quantification of LC × LC data is fundamentally a different process from that used for one-dimensional chromatography. This difference occurs because each compound injected onto the two-dimensional instrument is generally observed in more than one second-dimension chromatogram. In this section, we will assume a 100% duty cycle (i.e., 100% of the sample injected on the first-dimension column will be introduced into the second-dimension column and detected). The sampling process was discussed in some detail in Section 4.2. In the present section we use the modulation ratio, MR, given by Khummueng et al. as [150]



MR =

41σ ts

(4.49)

MR is inversely related to the dimensionless sampling time (ts / 1 σ) discussed in Section 4.2.1. The MR is a direct indicator of the number of peaks produced in  the second dimension from the analysis of a single compound by LC × LC [150]. The implications of this are that additional steps for peak integration are required beyond the typical baseline assignment and integration used for onedimensional separations. These steps include matching or assigning sequential second-dimension peaks to the correct parent peak [138], which may include an alignment process [151] as well as determining the peak size (or “volume”) from these multiple second-dimension peaks. Another complication is that peaks in the tails or fronts of the first-dimension peaks may be lost when the intensities of those peaks drop below the limit of detection [152]. This is the dilution effect, which is discussed in more detail in Section 4.4. Furthermore, because two-dimensional chromatographic methods are ideally suited for the analysis of highly complex mixtures, the successful resolution of overlapped peaks can be critical for obtaining satisfactory quantitative results. The multidimensional data structure of a two-dimensional chromatogram allows the use of powerful chemometric methods, such as parallel factor analysis (PARAFAC) and multivariate curve resolution (MCR) [115,153]. For many of these methods, temporal alignment of peaks in different samples will also be a critical issue [154]. In this section, we will discuss the challenges of quantification in two-dimensional chromatography from two perspectives. The first will be the determination of peak size, and the second will be the use of chemometric algorithms. We will also briefly discuss other chemometric tools developed for two-dimensional chromatographic analysis.

4.5.1  Quantification of Peak Intensity There is a fundamental difference in peak quantification in comprehensive twodimensional chromatographic methods as opposed to one-dimensional methods, as pointed out by Amador-Muñoz and Marriott in their 2008 review of quantification in comprehensive 2D-GC [152]. In one-dimensional separations, the integration of

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only a single peak is required, whereas in two-dimensional methods, the same compound (due to the modulation process) will be found in several sequential seconddimension chromatograms. This process is depicted in Figure 4.40(a). If the sampler (modulator) is functioning ideally, with a 100% duty cycle, the sum of the areas of the second-dimension peaks should equal the area of the corresponding one-dimensional peak by a one-dimensional separation method, as shown in Figure 4.40(c). Two parameters can affect the quantification of two-dimensional peaks that are illustrated in Figure  4.41: the modulation ratio, MR (Equation 4.49), and the sampling phase, ϕ, defined by Equation 4.6. Here, we consider a peak to be in phase if ϕ = 0, ±2π… (see bottom panels of Figure 4.41). Otherwise, it is sampled out of phase (shown in the top two rows of Figure 4.41). As previously shown in Figure 4.3, in-phase sampling gives rise to a symmetric peak pattern, whereas out-of-phase sampling gives an asymmetric pattern. It is possible that both the MR and ϕ affect the accuracy and precision of peak quantification [155]. Khummueng et al. [150] and Thekkudan, Rutan, and Carr [30] have studied the accuracy and precision of the area summation method for peak quantification using simulations. Amador-Munõz et al. also considered the summation of only selected second-dimension peaks [152]. A map of the accuracy and precision as a function of MR and ϕ provided by Thekkudan et al. [30] shows that the summation method provides precise results for a range of MR and ϕ values, but the accuracy of the summation method suffers at high modulation ratios, due to lack of detection of the small second-dimension peaks in the tails of the first-dimension peak [30]. The work of Amador-Munõz showed that using the three most intense modulated peaks in conjunction with an internal standard method permitted precise and accurate results to be obtained in the case where there was some overlap between the target analyte and its deuterated internal standard using a GC × GC method [152]. While the summation method described previously seems to work well for GC × GC data [152,156–158], it has been noted that the precision of replicate runs for LC × LC data is substantially degraded relative to 1D-LC data [29]. There is a fundamental difference in the nature of the sampling process in GC × GC as opposed to LC × LC. In GC × GC, typically a thermal modulator is used to introduce the cryogenically trapped sample onto the second-dimension column [158-159], whereas a valve-based modulator is used in LC × LC [21,130,160,161]. There is more of an opportunity for loss of sample between the first- and second-dimension systems with the valve-based system (if not optimized properly), resulting in inaccurate and imprecise quantitative results. Another feature of LC × LC separations as compared to GC × GC separations is that the second-dimension separation in LC × LC is typically much slower than in GC × GC, leading to a lower modulation ratio (unless a very slow first-dimension separation is used). This results in relatively low MR values being accessible using valve-based LC × LC systems. Another approach to quantification has been examined by Adcock et al. [162] and Thekkudan et al. [30], wherein the intensities (areas) of the 2D peaks are fit to a Gaussian model. In this method, the accuracy and precision of peak quantification as a function of MR and ϕ were better for the Gaussian fit than for the summation method, but an MR of greater than two must be used. At the lower modulation ratios, only one or two significant 2D peaks were observed; this results in an indeterminate © 2012 Taylor & Francis Group, LLC

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0

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5

0.5

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First Dimension Retention Time (min)

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Data Collection Time (s)

10

25

2

+

2 Area = 0.0 1t = 0.00 min R +

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Volume = 79.3 (Sum of Areas)

2

Volume = 80.1 (Gaussian fit of plotted points)

6 7 Se c –1 5 on 3 4 dD 4 in) 1 2 2 im e (m ens Tim ion 2 1 tion Re eten ten on R 0 0 si n e tio nT Dim im First e (s ) Fit Gaussian

=

Area = 0.0 1t = 1.75 min R

0 0 1 2 3 4 Second Dimension Retention Time

0.5

1

1.5

2

0 0 1 2 3 4 Second Dimension Retention Time

1

Area = 14.9 1t = 0.70 min R

0 0 1 2 3 4 Second Dimension Retention Time

+

2 1.5

0.5

Area = 0.0 1t = 0.35 min R

0.5

1

1.5

0 0 0 1 2 3 4 0 1 2 3 4 Second Dimension Retention Time Second Dimension Retention Time 2 Area = 0.0 1.5 1t = 2.10 min R 2 1 +

0.5

0 0 1 2 3 4 Second Dimension Retention Time 2 Area = 49.5 1.5 1 = 1.05 min tR 1 +

0.5

1

1.5 Intensity

Figure 4.40  (a) Appearance of the raw data in the form of sequential second-dimension chromatograms for a single chemical compound. (b) Data reformated to show the two-dimensional chromatographic peak. (c) Process for quantification by summing the second-dimension peak areas or by fitting the second-dimension peaks to a Gaussian peak shape. (Reprinted from Thekkudan, D. F. et al. 2010. Journal of Chromatography A 2010. 1217:4313–4327, ©2010, with permission from Elsevier.)

0

0.5

1

1.5

2

2.5

3

3.5

4

–0.5

0

0.5

1

1.5

(c) Intensity Intensity

2

Intensity

Intensity Intensity Second Dimension Peak Areas

Intensity

Second Dimension Retention Time (s)

Intensity

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Peter W. Carr, Joe M. Davis, Sarah C. Rutan, and Dwight R. Stoll MR = 1.6

MR = 3.2

φ=π

φ = 0.5π

φ=0

Figure 4.41  Figure illustrating how variations in MR and ϕ affect the relative peak areas of the sequential second-dimension peaks. For each case, the left panel shows the switching point for the valve or thermal modulation, and the right panel shows the pattern of relative peak areas of the sequential second-dimension peaks.

fit to the Gaussian function, which has three parameters. Fits using the exponentially modified Gaussian peak model have also been used to quantify two-dimensional peaks [163]. It was found that the peak width and tailing parameters correlated with the retention time, so only two parameters were needed to fit the first-dimension peaks to give accurate peak quantification [163]. Peak volume determination has also been used for quantification in comprehensive two-dimensional separations. Kallio and co-workers describe the calculation of the peak volume as “multiplying the data point height by the corresponding area and summing these subcolumns of the peak together” [164]. This process is illustrated in Figure 4.42. In principle, this approach should give identical results to the peak area summation approach, provided there are no errors in timing and that the

Area Data point height

Figure 4.42  Illustration of volume calculation for a two-dimensional peak. By multiplying the area by the data point height and summing these individual volume elements, the total peak volume is obtained. © 2012 Taylor & Francis Group, LLC

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same peak boundaries/baseline values are used in both cases. Hyötyläinen et al. have shown significant differences in the area summation and peak volume approaches for GC × GC analysis [159]; however, it is not clear to us whether these differences are due to differences in assigning a peak boundary (i.e., a square box in the case of the peak volume determination) or due to errors in the modulation timing. Another approach for peak quantification in comprehensive two-dimensional separations is the use of image analysis software, typified by the approach described by Reichenbach and his co-workers [165–168]. These researchers used the inverted “watershed algorithm” to determine peak volumes [168]. This method requires that adequate baseline correction be carried out and that the second-dimension peaks be aligned prior to analysis [169] (alignment issues will be discussed later in this section). This algorithm can be visualized as taking the negative of the two-dimensional peak and filling it to a constant level. This procedure is more akin to the volume determination method described earlier. While this approach has been used in GC × GC for quantification with some success [170], its application to LC × LC data has been somewhat problematic [171,172]. Another issue with this approach is that it does not impose any requirement for peak continuity (i.e., several discontinuous sections can be integrated in a given 2D chromatogram [169,171]). The preceding discussions have focused primarily on peak quantification, but do not address the necessary associated tasks of peak detection, baseline or background removal, and allocation of the 2D peaks to the appropriate parent peak. The issue of appropriate allocation of sequential 2D peaks is illustrated in Figure 4.43. The second-dimension peaks labeled a, b, and c show shifted (unaligned) 2D retention times, although all correspond to the same chemical compound. In order to integrate the two-dimensional peak correctly, the 2D peaks must be brought into registration (i.e., aligned) or at least assigned to the same parent peak. 2.6

2

2.4

g h 1

2tR (s)

2.2 2

a

b

c

d e

i

j

k

f

1.8 3.8

4

4.2 4.4 1t (min) R

4.6

Figure 4.43  (See color insert.) Two-dimensional chromatogram showing shifts in the second-dimension chromatograms, which complicate the assignment of second-dimension chromatograms to the correct parent peak. The points a, b, and c indicate sequential seconddimension chromatogram maxima that should be assigned to the same parent peak. (Reprinted from Peters, S. et al. 2007. Journal of Chromatography A 1156:14–24, ©2007, with permission from Elsevier.) © 2012 Taylor & Francis Group, LLC

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Some software packages that integrate these tasks with peak quantification have been reported. LECO Corporation has a software package, ChromatoTOF, which is designed to work with its GC × GC-TOF system. This software has been reported to give reproducible peak quantification results [173]. ZOEX Corporation provides the GC Image software [174], which is based on the algorithmic developments of Reichenbach and co-workers [165–168,175]. A version of this software is also available for LC × LC data [176,177]. Peters et al. have described an automated method that uses standard one-dimensional peak detection methods and employs a decision tree approach to merge the second-dimension peaks that should be associated with a single compound [138], as shown in Figure 4.43. This method has been used for the quantitative determination of triacylglycerols in corn oil [161] and has also been implemented for LC × LC by Stevenson et al. [132] specifically for the purpose of characterizing the performance of LC × LC methods. Mondello and co-workers have also developed a complete approach for analysis of LC  ×  LC data [178], which is now available commercially from Chromaleont [179]. This approach uses a “data triangle”-based integration method for the 2D chromatograms. Reichenbach has pointed out that this integration method gives identical results to a simple data point summation method, but is computationally less efficient [180]. Mondello et al. describe a method for assigning the second-dimension peaks to the correct parent compound; however, to us, the actual implementation of the approach is not clear. The approach is able to tolerate some drift in seconddimension retention times [178]. The aforementioned software has been applied to the quantification of polyphenols in red wines [181]. Kallio and co-workers have also described a software package for the analysis of 2D chromatograms, which includes capabilities for generating 2D and 3D plots, baseline assignment, and peak characterization (i.e., retention time determination) and quantification [164]. This program allows for both manual baseline assignment and automated peak detection. The option for manual peak integration is especially valuable because some investigators have found that manual integration provides much more reliable quantification than automated procedures [152,171]. An example of the baseline issues experienced in integrating second-dimension peaks is shown in Figure 4.44. In LC × LC, the use of rapid 2D gradients gives rise to substantial baseline issues, as seen in this figure. Despite the difficulties described here, there have been several applications of LC  ×  LC for quantitative analysis in sample matrices such as wine and juice [181,182], plant matrices [183,184], and atmospheric aerosols [185]. As software tools become increasing available, it is anticipated that quantitative power of LC  ×  LC methods will also improve.

4.5.2  Quantitative Analysis Using Chemometric Methods 4.5.2.1  Multilinear Methods The methods discussed in the previous section, while often using powerful graphics and image analysis tools, do not take advantage of the special structure of twodimensional chromatographic data. This data structure lends itself to analysis using very powerful algorithms [20,186]. Such algorithms allow badly overlapped peaks © 2012 Taylor & Francis Group, LLC

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Figure 4.44  Sequential second-dimension chromatograms showing the pronounced gradient baseline that complicates integration. Actual peaks are indicated by the arrows. (Adapted from Bailey, H. P., and Rutan, S. C. 2010. Chemometrics and Intelligent Laboratory Systems 106:131–141, ©2010, with permission from Elsevier.)

(R s < 0.5) that are inevitable and common when analyzing complex samples to be mathematically resolved by taking advantage of the inherent multidimensionality of the two-dimensional data structure. In the ideal case, a two-dimensional chromatographic peak can be represented as the outer product (⊗) of the 1D and 2D peak profiles as follows:

X = 1 c ⊗2 c

(4.50)

xij = ci ⋅ c j

(4.51)

or

where 1c (a function of the 1D time variable) represents the first-dimension chromatographic profile and 2c (a function of the 2D time variable) represents the seconddimension chromatographic profile [153]. The indices i and j refer to the temporal point numbers in the 1D and 2D, respectively. When N compounds are present, Equation 4.50 can be generalized as N

X=

∑c 1

n

⊗2 c n

(4.52)

⋅ 2 c jn

(4.53)

n =1

or

N

xij =

∑c 1

in

n =1

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1c

=

×

2c

×

=

Figure 4.45  Figure showing the data matrix X, which can be decomposed into the individual pure component first- and second-dimension chromatograms.

In this case, the data matrix X consists of the measured detector signals as a function of the times on the 1D and 2D columns. This data structure is referred to as “bilinear” and is depicted schematically in Figure 4.45. Two-dimensional liquid chromatographic data obey this data structure, provided that the retention times and chromatographic profile shapes for each individual component are identical in each of the sequential 2D chromatograms (i.e., there cannot be any overloading on the 2D column and experimental conditions must be sufficiently reproducible to provide extremely reproducible peak shapes). This explains why peak alignment is especially important when chemometric analysis is used. Note that “apparent” changes in retention times due to peak overlap or due to baseline shifts will not be a problem, as long as these effects are linearly additive. Data structures of this type can be decomposed using singular value decomposition (SVD) as follows [187,188]: X = USV T



(4.54)

where U contains the left singular vectors, V contains the right singular vectors, and S contains the singular values along the diagonal, with the off-diagonal elements equal to zero. The number of significant singular values indicates the number of distinct chromatographic components—that is, components with at least some differences in their first- and second-dimension profiles. SVD is frequently employed as a first step in the chemometric analysis of two-dimensional chromatographic data, often to estimate the number of overlapped chemical components present in a two-dimensional chromatogram containing overlapped peaks. One or more mathematical components might be needed to represent the contribution of the chromatographic background to the signal. It is our belief that the real power of the chemometric approaches for the analysis of two-dimensional chromatographic data comes when multiple samples are simultaneously analyzed in a series of two-dimensional chromatograms. What happens here is that information as to the relative amount (concentration) of each species in the different samples is obtained directly from the algorithm, without the need to integrate the peaks separately. For the analysis of multiple samples simultaneously, the data take on a trilinear structure, as follows: N

X=

∑c 1

n

⊗2 c n ⊗ a n

(4.55)

n =1

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or N

xijk =

∑c 1

in

⋅ 2 c jn ⋅ akn

(4.56)

n =1



Here, an is a vector of the relative concentrations of the nth component present in each of the K different samples injected into the two-dimensional instrument. Chromatographically, the trilinear structure means that retention times and chromatographic profiles for each individual component not only must be identical for the 1D and second 2D separations within a particular two-dimensional separation, but also must be consistent over the course of the entire analysis of all samples; that is, there cannot be any overloading of the 2D column and experimental conditions must be sufficiently reproducible over the course of the experiment to produce extremely reproducible peak shapes. In essence, there can be no drift in retention times or peak shapes on either dimension due to any source including irreversible binding of chromatographic garbage. Methods such as generalized rank annihilation (GRAM) [153,154,189–194], trilinear decomposition (TLD) [195,196], and parallel factor analysis (PARAFAC) [115,197–203] offer a powerful means of analyzing trilinear data sets. These algorithms operate on the raw data contained in the three-way data array, X; they provide as their solution the chromatographic and concentration profiles for the components contributing to the data. Provided that the sample set includes both calibration standards and unknowns, quantitative information is obtained directly from these procedures. A further enhancement of the data structure is possible when multichannel detection is employed. In GC × GC experiments, this usually is accomplished using timeof-flight mass spectrometry (TOF-MS) [173,198,199,204–206]. However, in LC × LC, diode array detection (DAD) is frequently used [115,130,171,172,176,182,196], although MS detection in LC × LC is starting to be used more frequently [184,185]. In the case of this additional spectral information, the data structure can be represented as follows: N

X=



∑c 1

n

⊗ 2 cn ⊗ an ⊗ sn

(4.57)

n=1

or N

xijk =

∑c 1

in

⋅ 2 c jn ⋅ akn ⋅ sn

(4.58)

n =1

where s n contains the spectral responses for the nth component present in the samples. © 2012 Taylor & Francis Group, LLC

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Such data are quadrilinear, provided that the retention times and chromatographic profile shapes for each individual component are identical in both the 1D and 2D separations as described before. For the resulting quadrilinear data, PARAFAC is the method of choice, provided that the assumptions of quadrilinearity are upheld in practice [115]. The power of PARAFAC analysis for trilinear and quadrilinear data is derived from the fact that a unique, chemically reasonable solution is obtained for the component chromatographic, spectral, and concentration profiles. Unfortunately, in practice, the data structure does deviate significantly from tri- or quadrilinearity, so alternative data analysis strategies must be developed. These strategies typically follow one of two directions: (1) use of algorithms (e.g., MCR-ALS) that do not have tri- or quadrilinear requirements for the data, or (2) preprocessing the data to align them to provide the necessary tri- or quadrilinear structure. 4.5.2.2  Bilinear Methods Of the requirements for observing quadrilinear behavior in comprehensive twodimensional chromatography, it is much more likely that spectral peak shapes will be more consistent than will the 1D and 2D peak profiles, especially in the case of DAD detection for LC × LC experiments. (MS detection in LC × LC is not as reproducible, so this may preclude the use of some chemometric algorithms for these data.) Therefore, a bilinear model is often appropriate for these data, expressed as N

X=

∑c

n

⊗ sn

(4.59)

⋅ sn

(4.60)

n =1

or N

xij =

∑c

in

n =1

where cn now consists of the sequential 2D chromatograms for one or more injections. This means that the information contained in 1cn, 2cn, and a is all contained in a series of second-dimension chromatograms in the vector c. Analysis of a data matrix, X, with this data structure can be accomplished using SVD, but the results are referred to as “abstract” because the singular vectors contained in the U and V matrices are linear combinations of the true pure chromatographic and spectral profiles. Multivariate curve resolution (MCR) procedures offer a means to obtaining the true pure component profiles by using chemically meaningful constraints. Solutions to the constrained model are usually obtained using an alternating least squares (ALS) algorithm [207–213]. Constraints that can be used include non-negativity, unimodality, and selectivity [210]. Bailey and Rutan have implemented an MCR-ALS approach for the analysis of LC × LC-DAD data using an iterative key set factor analysis (IKSFA) [214] method to generate the starting conditions for MCR-ALS [172]. These authors analyzed a set of replicate sample injections and were able to obtain good reproducibility in the © 2012 Taylor & Francis Group, LLC

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resolution of overlapped peaks. In a specific part of the two-dimensional chromatogram, over 50 peaks were detected with an ideal peak capacity based on the product rule (Equation 4.1) of 48. Of these 50 peaks, 34 were quantified, with precisions ranging from 1% to 15% RSD [171,172]. 4.5.2.3  Retention Alignment Methods Alignment strategies are a second approach that are frequently used to pretreat data that are affected by retention time shifts in both the first- and second-dimension separations [151,154,192,215–218] prior to subjecting the data to chemometric quantification. Alignment algorithms have been used that are based on detection of the reduction in rank (i.e., a reduction in the number of significant singular values) as data are shifted and come into alignment with one another [154,219]. Skov et al. reported on a local shift correction routine based on correlation and followed correction with PARAFAC analysis [218]. These authors compared those results with the results from a PARAFAC2 analysis, which is an algorithm that is relatively insensitive with respect to retention time shifts in one dimension [201,218,220]. The method of correlation optimized warping (COW) has also been used for alignment of two-dimensional chromatograms [217,221]. This is a more global approach than that used by Skov et al., but a difficulty with the COW technique is that there needs to be a high degree of commonality between the chromatograms that are to be aligned, or erroneous results will be obtained. Reichenbach et al. have used well known image analysis transform techniques to align GC × GC chromatograms [165,175]. Retention time shifts between two chromatograms are modeled using multiple linear equations, but peaks common to both chromatograms must be identified to determine the model parameters, which are then used to align all other peaks. This technique has been shown to work well for retention time shifts caused by changes in oven temperature ramp rate and inlet pressure in GC × GC [165]. Despite the difficulties outlined previously, chemometric methods are becoming much more useful for solving practical data analysis problems. Synovec and coworkers have successfully used the PARAFAC analysis of GC × GC data to characterize yeast metabolism [204,222,223]. In addition, these researchers have made important strides in automating the implementation of these methods [198,199,224]. It should be pointed out that the application of these methods to LC × LC data lags significantly behind that of GC × GC. This is likely due to the fact that retention time shifts appear to be more problematic in LC × LC methods, and that the generally higher degree of undersampling in the 1D separation in LC × LC compared to GC × GC makes the implementation of shift correction more difficult.

4.5.3  Other Chemometric Methods One potentially very valuable application area for GC × GC and LC × LC technologies is metabolomics. Of frequent interest in metabolomic studies is the comparison of different samples to identify those metabolites that exhibit significant changes in concentration in response to a biological stimulus. Pierce et al. have described a data analysis approach based on a Fisher ratio analysis to discover previously unknown chemical differences between different samples based on comprehensive © 2012 Taylor & Francis Group, LLC

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two-dimensional separation data [225]. Principal component analysis has also been used for this purpose [226]. Chemometric methods can be used to find related compounds, such as a series of homopolymers, based on trends in retention in a two-dimensional chromatogram [227]. As an example, consider an LC × LC chromatogram of a series of a homopolymer. The chemical property of interest is the molecular weight. The retention times on the two chromatographic systems will be correlated because this is a one-dimensional sample, following the sample dimensionality argument of Giddings [45] (see Section 4.3.1). The chemical variance approach described by Vivó-Truyols and Schoenmakers [227] seeks to transform the correlated retention behavior to a trend along the axis of interest—in this case, molecular weight. This approach was applied successfully to the RPLC × SEC analysis of functional poly(methyl-methacrylate) polymers with different numbers of hydroxyl end groups and degrees of polymerization [227]. Another important application is locating, within the two-dimensional separation space, those peaks that are spectrally similar to some target compound. The DotMap algorithm developed by Synovec and co-workers [228,229] identifies the locations within two-dimensional chromatograms where compounds with the selected target spectrum elute. This approach is based on calculating a dot product of the baseline corrected, scaled, weighted, and normalized mass spectrum of the target with the mass spectra at every location within the two-dimensional chromatogram. A related method based on window target testing factor analysis (WTTFA) was developed by Porter et al. to identify chromatographic peaks matching a particular UV-visible spectrum of interest [115]. These tools will go a long way in making comprehensive two-dimensional separations useful for the comparison of complex mixture samples of interest in metabolomic studies.

4.6  Comparison of 1D-LC and LC × LC Historically, there has been little debate about the potential improvement in the resolving power of liquid chromatography by extending the technique to multiple dimensions of separation. The early descriptions of this potential by Giddings [27] and others [230,231] have been embraced by the community and are essentially the same as those used today (see Equation 4.62). However, the relationship between this theoretical potential and what has been and can be achieved in practice has received much less attention, arguably to the detriment of the advancement of the field of multidimensional separations in general. Indeed, as pointed out by Blumberg et al. [34] and Davis [89], reports on the performance of LC × LC systems often essentially assert that the performance of the LC × LC system studied must be better than a conventional one-dimensional separation, simply because it is a two-dimensional separation. There is no question that there have been many excellent studies of LC × LC separations where the observed performance is in fact significantly better than what can be achieved with a conventional one-dimensional separation in a similar analysis time. However, in the foreseeable future (barring significant engineering breakthroughs), conventional one-dimensional separations will always be superior

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to LC × LC for very fast analyses (e.g., 2 h), then it will be useful, but it will remain the niche technique that it has thus far been. Finally, we assert that the dominance of one mode over the other is heavily dependent on two important factors: • the nature of the separation problem at hand, because some separation problems and some mixtures are inherently better suited to one mode over the other. • proper optimization of each method because it certainly is possible to execute a poorly designed LC × LC separation that will yield much less performance (as measured by numbers of resolved peaks, peak capacity, etc.) than a well-designed one-dimensional separation of the same sample in the same analysis time. The objective of the following section is to describe a framework and metrics needed for equitable comparisons of conventional one-dimensional and LC × LC separations and to summarize some of the most recent experimental results in this area.

4.6.1  Metrics of Separation Performance A number of metrics of separation performance are useful for comparing one- and two-dimensional separations, including peak capacity, numbers of observed peaks, and the resolution of particular pairs or groups of peaks. Numbers of peaks and the resolution of particular peaks are the most direct, practical measures of performance; however, they are also highly application specific and generally must be determined experimentally. On the other hand, peak capacity lends itself more readily to theoretical prediction and is used to guide optimization calculations, as discussed in Section 4.4. There is no question that practically useful estimates of peak capacity are dependent on the sample and separation problem at hand. Nevertheless, peak capacity is a far more general metric than either the numbers of peaks observed for a particular sample or resolution of a particular pair of peaks. In some cases, the ordered structure of LC × LC chromatograms with respect to chemical functionality of the analytes of interest is a valuable feature of the two-dimensional separation that, by definition, is simply not available in the one-dimensional case [227]. This characteristic of the separation quality is much more difficult to measure than the other metrics and is highly sample and application specific. © 2012 Taylor & Francis Group, LLC

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4.6.1.1  Peak Capacity The theoretical background concerning the calculation of peak capacity of one- and two-dimensional separations was discussed in Sections 4.2–4.4. Important aspects of these calculations are repeated here for convenience. The essential value of peak capacity as a metric of performance is that it represents the maximum number of chromatographic peaks that can be “fit” side by side with some specified resolution into the one- or two-dimensional separation space. The salient features of these calculations are repeated here for clarity. The calculation of one-dimensional gradient peak capacity (see Section 4.4) is very straightforward in that it is simply the ratio of the portion of the separation space that contains peaks to some measure of the peak width:



nc ,1D =

t R.last − t R , first w

(4.61)

where tr,first and tr,last are the positions of the peaks observed at the limits of the retention window, and w is a measure of the average peak width (4σ). Equation 4.61 is the same as Equation 4.16, except that the contribution of the void peak is neglected. Calculation of the useful peak capacity of LC × LC separations is considerably more difficult for two primary reasons. First, the inevitable undersampling of firstdimension peaks effectively reduces the contribution of useful peak capacity to the two-dimensional separation by the first dimension (see Section 4.2). Second, defining the usable portion of the two-dimensional separation space is more difficult simply because it is a two-dimensional problem (see Section 4.3). The peak capacity of an ideal LC × LC separation (assuming infinitely fast sampling and complete usage of the separation space) is given by the so-called product rule, Equation 4.1 [231]:

nc ,2 D = 1nc × 2 nc

(4.62)

The deleterious effects of undersampling and incomplete usage of the separation space (see Sections 4.2 and 4.3) are accounted for by (1) dividing 1nc by a factor that accounts for the average effective broadening of first-dimension peaks as a result of the infrequent transfer of aliquots of first-dimension effluent to the seconddimension column, and (2) multiplying the product of the peak capacities by the “fractional coverage,” fcov (ranging from 0 to 1; see Section 4.3). This gives the effective two-dimensional peak capacity nc*,2 D (cf. Equations 4.2 and 4.13):



nc*,2 D =

1

nc × 2 nc × fcov

(4.63)

We firmly believe that the fair comparisons of conventional 1D-LC and LC × LC separations on the basis of peak capacity should be made using peak capacities calculated using Equations 4.61 and 4.63. Failure to use these numbers unfairly favors one mode over the other. © 2012 Taylor & Francis Group, LLC

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The two most thorough comparisons of conventional one-dimensional and comprehensive two-dimensional separations we are aware of to date were reported by Blumberg and co-workers [34] and ourselves [29], and we discuss them in turn in the following sections. A recent paper by Eeltink et al. [139] describes the comparison of 1D-LC and off-line 2D-LC applied to proteomics. Both off-line separations and proteomics applications are beyond the scope of this chapter; however, the paper is very useful for these areas, and we refer readers to it if they are particularly interested in proteomics applications. Although the Blumberg paper describes a comparison of 1D-GC and GC × GC, we feel it is very thorough and the fundamental issues related to performance comparison are sufficiently similar to those encountered in online LC × LC that it warrants discussion here. 4.6.1.2  Blumberg Comparison In their comparison of 1D-GC and GC × GC, Blumberg and co-workers carefully optimized both the one- and two-dimensional methods with the goal of resolving as many of the constituents of a synthetic mixture of 131 semivolatile compounds as possible in an analysis time of 110 min. Each method was optimized such that a comparable detection limit would be obtained for the two methods. They then compared the performance of the two techniques in terms of estimated peak capacities and the number of constituents of their mixture predicted to be separated with a resolution of one or greater using statistical overlap theory (see Section 4.2). The calculated peak capacities of the one- and two-dimensional methods were 1,320 and 5,440, respectively. Although their approach to the calculation of the twodimensional peak capacity was somewhat different from that expressed by Equation 4.63, we believe the outcome is more or less the same with respect to accounting for the effective broadening of first-dimension peaks due to undersampling. Given our definition of fractional coverage of the separation space, fcov in their work was practically 1 for the separation of the semivolatile mixture (see Figure 4.46). Although the peak capacity of the two-dimensional method is about four-fold higher than that of the one-dimensional method, the practical utility of the added peak capacity is compromised by the disproportionate clustering of a large fraction (33%) of the sample constituents in a small fraction (2.5%) of the two-dimensional separation space; this will be discussed more later (see the peaks circled by the ellipse in Figure 4.46). First, it is instructive to examine the reasons that a larger improvement in peak capacity is not obtained upon the addition of the second dimension of separation, as improvements of more than 10-fold are predicted by GC × GC theory (see Equation 35 in reference 34). Blumberg et al. clearly show that the single largest impediment to the realization of these large increases in peak capacity is the relatively slow performance of existing modulators used to re-inject portions of first-dimension effluent into the second-dimension column. This is a devastating effect because the large temporal variance (σm ~ 50–100 ms) of the injection pulse overwhelms the very narrow peak widths that are expected in the second dimension (2σ < 10 ms), resulting in much lower than expected peak capacities. The conventional approach to overcome this is to make the second dimension analysis time much longer (e.g., 5 s compared to 1 s) such that the variance of © 2012 Taylor & Francis Group, LLC

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1/3 of all compounds

Column bleed 100 min

Figure 4.46  (See color insert.) GC × GC chromatogram showing the separation of a mixture of 131 semivolatile compounds from the comparison of 1D-GC and GC × GC by Blumberg et al. The region encompassed by the ellipse represents about 2.5% of the separation space, but contains peaks for about one-third of the compounds in the mixture, showing the uneven distribution of peaks in the two-dimensional separation space for this sample. (Reprinted from Blumberg, L. M. et al. 2008. Journal of Chromatography A 1188:2–16, ©2008, with permission from Elsevier.)

the injection pulse contributes a smaller fraction of the total variance of the seconddimension peak. This is an effective approach to dealing with this problem; however, this is not without other consequences. Increasing the sampling time from 1 to 5 s induces significant broadening of otherwise narrow first-dimension peaks (1σ ~ 1 s in the optimized one-dimensional case; see Table  3 in reference 34) via the undersampling phenomenon. The early work of Murphy et al. [28] on the undersampling problem has led to a mind-set that often leads researchers to adjust operating conditions in GC × GC and LC × LC experiments such that first-dimension peaks are sampled three to four times across their first-dimension width, producing peaks for a given sample constituent in three to four consecutive second-dimension chromatograms. In many cases, as in the Blumberg study, this leads researchers deliberately to broaden first-dimension peaks [11,232,233] to satisfy this sampling requirement. This is the first and often significant reason that the potential of the two-dimensional separation is not realized, in that the contribution of the first dimension to the total peak capacity is compromised; thus, some of the peak capacity contributed by the second dimension is “spent” recovering the peak capacity that was sacrificed in the first dimension to satisfy the sampling criterion described before. It is worth noting here that the most recent optimization studies of LC × LC [37,41,90] suggest that the number of fractions per first-dimension peak that optimizes LC × LC peak capacity © 2012 Taylor & Francis Group, LLC

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Figure 4.47  (See color insert.) GC chromatograms showing the elution of several semivolatile compounds from the comparison of 1D-GC and GC × GC by Blumberg et al. Panel (a) shows the separation of 18 compounds by fully optimized 1D-GC; all compounds in this window are baseline resolved. Panel (b) shows the separation of the same compounds using the first dimension only of a GC × GC system where the peaks have been deliberately broadened in 1D to accommodate the relatively slow speed of the 2D separation. In this case, the resolution of several compounds is significantly deteriorated. The contour plot shows the GC × GC chromatogram for the same group of compounds obtained by adding a 2D separation to the 1D-GC separation shown in panel (b). The chromatogram in panel (c) is the 1D chromatogram reconstructed by a linear interpolation of the average concentrations of fractions along the 1D axis. As in the transition from panel (a) to (b), even more resolution along the 1D axis is lost in the move from panel (b) to (c) because of undersampling of the 1D peaks. Even after the addition of the 2D separation, some of the compounds separated in (a) are not separated in the GC × GC chromatogram (e.g., peak pairs 57/58 and 44/47). (Reprinted from Blumberg, L. M. et al. 2008. Journal of Chromatography A 1188:2–16, ©2008, with permission from Elsevier.)

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is closer to the two to three range, rather than four, which has been most recognized historically as a result of the work of Murphy et al. [28]. It seems that strict adherence to this guideline is not always necessary and, in fact, may be detrimental in some cases. From the perspective of the undersampling theory discussed in Section 4.2, the impact of undersampling on first-dimension peak capacity is nearly independent of whether or not first-dimension peaks are deliberately broadened to satisfy the sampling criterion. This is not to say that there are not other effects that stem from severely undersampled first-dimension separations. Indeed, it has been shown that the precision of quantification LC × LC separations improves as the number of samples of a first-dimension peak increases from one to an optimum of two to three when a Gaussian fit is used to describe the 1D prefile [30]. Also, the potential for application of sophisticated multiway chemometric methods to further resolve chromatographically under-resolved peaks is contingent on the appearance of peaks for a particular sample constituent in more than one adjacent second-dimension chromatogram. The impact of deliberately broadening the first-dimension peaks (panel b) and the undersampling (panel c) on the first dimension of the GC × GC separation from Blumberg’s work is shown in Figure 4.47 compared to the performance of a highly optimized 1D-GC separation (panel a) of the same sample. The obvious consequence of these compromises is the loss of resolution in the first dimension. For example, peaks 55 and 56 are resolved to baseline in the 1D-GC case, but it is barely evident that two peaks are present after the deliberate broadening of first-dimension peaks, and all resolution is lost after undersampling. The authors’ estimate of the total degradation in the peak capacity of the first dimension is about a factor of 3.7 decrease. In this case, then, 3.7 units of second-dimension peak capacity are spent recovering peak capacity lost in the first dimension; the remaining second-dimension peak capacity constitutes the actual increase in peak capacity over the optimized 1D-GC separation, in this case a factor of four. In addition to describing the reasons for the less than expected increase in peak capacity of the GC × GC separation over the optimized 1D-GC separation, the authors examine the effect of the peak distribution in the GC × GC separation of the 131-component semivolatile mixture on the net resolution of constituents of the sample. Figure 4.46 shows that while essentially the entire two-dimensional separation space is occupied by peaks, making fcov unity in Equation 4.63, the distribution of peaks is not at all uniform, with about 33% of the compounds eluting in a small area that constitutes only about 2.5% of the available space. The consequences of this uneven distribution are then explored for the 131-component mixture studied in this work. Using statistical overlap theory (see Section 4.2), they predict the numbers of sample constituents present in peak clusters (overlap of two or more constituents) in the 1D-GC chromatogram and in two distinct regions of the GC × GC chromatogram. The calculations predict 23 constituents present in clusters in the one-dimensional case (or 108 resolved peaks), just 3 unresolved constituents in the uncrowded region of the GC × GC chromatogram, but 17 unresolved constituents in the crowded region. The statistical significance of the difference between the number of resolved peaks in the 1D-GC and GC × GC cases (108 versus 105, respectively) is questionable. The authors use these results as the ultimate evidence that GC × GC is not © 2012 Taylor & Francis Group, LLC

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clearly superior to 1D-GC, provided that the one-dimensional separation is highly optimized. Obviously, this conclusion is strongly dependent on the complexity of the sample under study and the analysis time of both methods, but to the extent that different sample types exhibit the kind of uneven peak distribution shown in Figure 4.46, their argument seems quite widely applicable. 4.6.1.3  Stoll and Huang Comparisons In our own work [29], we have carefully compared the performance of conventional 1D-LC and LC × LC separations of a water-soluble extract of maize seed. There are some similarities to the study of Blumberg and co-workers; however, some significant differences are summarized in Table 4.6. The premise of our comparison was to examine the benefit of adding a second dimension of separation to a one-dimensional separation that was previously optimized for a 5 μm particle size. This required changes in some of the operating parameters, such as significantly decreasing the first-dimension flow rate to avoid prohibitively large injection volumes in the second dimension of the system. This kind of compromise is unavoidable in online LC × LC systems because of the tight linkages between the first and second dimensions of the system. The scope and nature of these compromises has been very clearly articulated most recently by VivóTruyols et al. [37]. In our work, we used Equations 4.61 and 4.63 to calculate the peak capacities of the one-dimensional and LC × LC separations, respectively. In this case we attempted to optimize the second dimension of the LC × LC system by finding the conditions (particularly the gradient time) that maximized the productivity of the second separation (peak capacity/time), and held those conditions constant even at different total LC × LC analysis times. The same physical sample was used for all of the separations, and UV-visible absorbance detection at 210 nm was employed. The primary findings

Table 4.6 Differences between One- and Two-Dimensional Comparisons of Blumberg et al. and Stoll et al. Aspect of Study Sample type Points of comparison Metrics used for comparison One-dimensional separation

Blumberg et al.

Stoll et al.

Synthetic: 131 known compounds One time point: 110 min. Effective peak capacity, number of resolved peaks predicted from SOT Fully optimized for onedimensional analysis

Unknown: several hundred detectable compounds Three time points: 15, 30, and 60 min Effective peak capacity, number of resolved peaks counted in chromatograms Optimized one-dimensional separation using the same particle size as in the first dimension of the two-dimensional system

Sources: Blumberg, L. M. et al. 2008. Journal of Chromatography A 1188:2–16; Stoll, D. R. et al. 2008. Analytical Chemistry 80:268–278.

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Figure 4.48  Comparison of 1D-LC and LC × LC separations of the same physical sample of maize seed extract in terms of the estimated effective peak capacity (�) and the number of peaks counted (⚬) in the respective chromatograms. At all analysis times studied, in this experiment the LC × LC separation is superior to the 1D-LC separation, though the difference diminishes as the analysis time is decreased, suggesting a crossover time below which the 1D-LC method becomes superior. (Reprinted with permission from Stoll, D. R. et al. 2008. Analytical Chemistry 80:268–278, ©2008 American Chemical Society.)

of our study are shown in Figure 4.48, where the ratios of peak capacities of the onedimensional and LC × LC separations, and the numbers of peaks counted in those separations, are plotted as a function of the total analysis time of each separation. The figure shows that the LC × LC separation is superior to the comparable onedimensional separation at the same analysis time for all 1D times studied, both in terms of the estimated peak capacity and the numbers of peaks counted in the chromatograms. The solid lines are extrapolations of the peak capacity and peak number trends to shorter analysis times that show that a conservative estimate of the analysis time beyond which LC × LC is superior to 1D-LC is 10 min. One of the biggest shortcomings of this study is that, unlike the Blumberg study, which compared the GC × GC separation to a fully optimized 1D-GC separation, we compared the LC × LC separation to a 1D-LC separation where the particle size used in the one-dimensional case was the same as that used in the first dimension of the LC × LC separation. This invites questions about what this comparison would look like (as a function of time) if the one-dimensional separation were truly optimized, including the selection of particle size. However, even if the peak capacity of the 1D-LC separation were doubled as a result of such optimization (which is quite liberal considering the behavior of the nonpeptide molecules studied and in light of other work on the optimization of peptide separations [9,135]), the LC × LC separations would still be superior (in terms of peak capacity) to the one-dimensional ones at all analysis times longer than about 15 min. © 2012 Taylor & Francis Group, LLC

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Figure 4.49  Comparison of 1D-LC (♦) and LC × LC separations of the same physical sample of maize seed extract in terms of the estimated effective peak capacity of each separation. Sampling times in the LC × LC experiments were 21 (⚬), 12 (Δ), 40 (⬨), or 6 (◽) s. At all analysis times studied in this experiment, the LC × LC separation is superior to the 1D-LC separation for at least some sampling times. These experimental results show that selection of the proper sampling time is very important in maximizing the LC × LC performance, both in absolute terms and relative to the 1D-LC separation. (Reprinted from Huang, Y. et al. 2011. Journal of Chromatography A 1218:2984–2994, ©2011, with permission from Elsevier.)

In a recent extension of our initial comparison, Huang et al. [134] compared the effective peak capacities of LC × LC separations of a maize seed extract with varying sampling times to optimized 1D-LC separations of the same sample at analysis times in the range of 5–50 min. In contrast to our early work in which the sampling time was fixed at 21 s, in the study of Huang et al. the sampling time was varied from 6 to 40 s, at all LC × LC analysis times. As the second-dimension reequilibration time was held at 3 s, the shortest second-dimension gradient time was 3 s. The effective LC × LC peak capacities shown in Figure  4.49 constitute experimental verification that optimal sampling times exist and that these optimal times depend on the performance of the 1D separation. Interestingly, the results of this work also show that the utilization of the two-dimensional separation space changes significantly with changes in sampling time, an important consequence that is fundamentally independent of the effect on the peak capacity through as described in Section 4.2. An example of the dependence of the LC × LC peak capacity on sampling time is shown in Figure 4.38 and has been extensively discussed previously [29]. Not only is there an optimum sampling time at each LC × LC analysis time, but the results in Figure 4.49 also show that the superiority of LC × LC over 1D-LC at a given analysis time depends heavily on which sampling time is used. For example, at an analysis time of 10 min, a sampling time of 12 s yields an LC × LC separation with roughly two-fold more peak capacity than the corresponding 1D-LC separation. However, a © 2012 Taylor & Francis Group, LLC

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sampling time of 6 s reduces the peak capacity of the 2D separation so much that the LC × LC separation becomes inferior to the 1D-LC separation. Finally, we point out that this study confirms the earlier prediction that for separations of low molecular weight compounds the performance of LC × LC exceeds the performance of 1D-LC separations at analysis times exceeding 5–10 min, as long as the LC × LC separation is properly optimized. It is instructive to examine the origins of the decrease in the peak capacity ratio at short analysis times that are evident in Figure 4.48. Figure 4.50 shows that a significant fraction (44% to 62%) of the available onedimensional peak capacity is lost upon converting to an LC × LC separation simply because suboptimal conditions must be used in the first dimension to allow interfacing with the second dimension of the system; this fraction increases as the total analysis time decreases. The second effect that increases in severity with decreasing total analysis time is the loss of first-dimension peak capacity due to undersampling, which ranges from an additional 35% to 70% loss. The origins of these losses are analogous to those described in the work of Blumberg et al.; however, we do not know about differences in the dependence of the losses on analysis time because they only studied one time point. We believe that both of these losses are problems that are solvable to some extent, but there are finite limits to what can be done. For example, the use of narrower columns in the first dimension of the LC × LC system in our study would permit the use of flow rates nearer to the optimal flow rate while still allowing a successful interface to the second dimension. However, the use of narrower columns limits the sample loadability and therefore affects the detection limits; these are complex trade-offs. It should be pointed out in this context that the use of low flow rates in the first dimension relative to that used in the second can allow use of marginally miscible eluents [11,50,112]. On the other hand, the impact of undersampling can be reduced by using shorter sampling times. This effectively increases the peak capacity of the first-dimension separation, but it also decreases the peak capacity of the © 2012 Taylor & Francis Group, LLC

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second-dimension separation; thus, the two effects oppose each other, representing yet another compromise. 4.6.1.4  Numbers of Observed or Resolved Peaks As shown in Figure 4.48, we have used the number of observed peaks as a metric for comparing 1D-LC and LC × LC. Several other groups have used this metric as well; however, most studies have not been designed in a way that allows head-to-head comparison of one- and two-dimensional methods on the basis of the number of resolved peaks per unit of analysis time. As is the case with the use of peak capacity as a metric, some of the more detailed comparisons of one- and two-dimensional separations in terms of the number of resolved peaks are found in the GC × GC literature. One good example involves the difficult separation of polychlorinated biphenyl (PCB) congeners, which is an application of GC × GC that has received considerable attention [234]. In this case, the goal of the separation is to resolve as many of the 209 target congeners chromatographically as possible. While a high peak capacity is certainly beneficial in this pursuit, the number of resolved target compounds is a more practically meaningful measure of the performance of the method. In a 2004 study, Focant, Sjödin, and Patterson [234] reported the resolution of 192 of the 209 congeners in a GC × GC analysis time of 143 min. This has been followed more recently by some very efficient 1D-GC separations of the same compounds [235] showing that 195 of the 209 congeners can be resolved in 95 min after chemometric curve resolution of chromatographically overlapped peaks. The point is made in this case that comparable separations of this complex mixture are possible by 1D-GC and GC × GC and that neither separation is clearly superior despite the high potential peak capacity of the GC × GC separation.

4.7  Summary and the Future There are many unresolved issues related to the principles of comprehensive online multidimensional chromatography as well as many unsolved experimental problems. In our view, the fact that the resolving power of LC × LC can be, under some conditions, superior to optimized 1D-LC has been conclusively demonstrated. However, as pointed out in Section 4.6, it is not yet clear that LC × LC is generally superior to 1D-LC at times sufficiently short to move LC × LC from a niche technique to the point where it will be the dominant mode of LC for the majority of LC analyses. Certainly, its superiority has been demonstrated at times as short as 5–10 min by the resolution of maize seed extract [29,134]. However, its superiority has not been demonstrated for a convincingly large variety of sample types. Additionally, there have been so few quantitative applications (e.g., references 29, 181–185) of LC × LC that it is very unclear if LC × LC can or will ever provide the high precision ( 0............................................................. 332 7.3.4.9 Values of C-2.8 < 0............................................................. 334 7.3.4.10 Values of C for Other Columns.......................................... 335 7.3.5 Hydrogen Bonding α′B...................................................................... 335 7.3.5.1 Solute Hydrogen-Bond Acidity α′..................................... 335 7.3.5.2 Column Hydrogen-Bond Basicity B versus Hydrophobicity H................................................................ 338 7.3.5.3 B versus H for Other Column Types...................................340 7.3.5.4 B as a Function of Column Properties (Type-B Alkylsilica Columns)............................................ 341 7.3.5.5 The Origin of Hydrogen-Bond Basicity for Different Columns.............................................................................. 341 7.3.5.6 Values of B for other Columns............................................ 343 7.3.6 Other Solute–Column Interactions.................................................... 343 7.3.7 Error in the Model.............................................................................344 7.4 Applications of Column-Selectivity Measurements......................................346 7.4.1 Comparing Columns in Terms of Selectivity.................................... 347 7.4.2 Choosing Columns of Similar Selectivity......................................... 349 7.4.3 Choosing Columns of Different Selectivity...................................... 351 7.4.4 Anticipating Peak Tailing.................................................................. 352 7.4.5 Design of Columns with Unique Selectivity..................................... 353 7.4.6 Control of Column Manufacture....................................................... 355 7.4.7 Stationary-Phase Degradation........................................................... 356 7.4.8 Identifying Column Type................................................................... 356 7.4.9 Predictions of Retention as a Function of the Column...................... 356 7.4.10 Miscellaneous Other Applications.................................................... 358 7.4.10.1 “Slow” Column Equilibration............................................. 358 7.4.10.2 Stationary-Phase “De-wetting”........................................... 360 7.5 A Comparison of Different Procedures for Describing Column Selectivity.................................................................................... 360 7.5.1 Number of Columns in the Database (Requirement 2 in Table 7.10)...362 7.5.2 Types of Columns in the Database (Requirement 3 in Table 7.10)......362 7.5.3 All Solute–Column Interactions Measured? (Requirement 4 in Table 7.10)...................................................................................... 363 7.5.4 Measurement of Specific Solute-Column Interactions (Requirement 5 in Table 7.10)............................................................ 363 7.5.5 Relation of Column Selectivity to Stationary-Phase Composition (Requirement 6 in Table 7.10).......................................364 7.5.6 Predictions of Retention....................................................................364 7.5.7 Summary...........................................................................................364 7.6 Conclusions.................................................................................................... 365

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Acknowledgments................................................................................................... 366 Appendix 7.1: Routine Measurement of Column-Selectivity Parameters H, S*, A, B, and C................................................................................................... 366 Appendix 7.2: Dependence of Column Selectivity on Column Properties............ 368 Symbols.................................................................................................................. 371 References............................................................................................................... 372

7.1  Introduction Separation selectivity is central to the use of reversed-phase chromatography (RPC). Some examples of selectivity are illustrated by the three separations of Figure 7.1, where only the column is varied. The two separations of Figure  7.1(a, b) show very similar separation, except that all peaks are more retained in Figure 7.1(b). A decrease in flow rate for the separation of Figure  7.1(a) by 20% would yield two, almost identical separations. In this case, the selectivity of the two separations is quite similar. The chromatogram of Figure 7.1(c), on the other hand, shows major changes in the arrangement of peaks compared to Figure 7.1(a, b—that is, a marked 2 4

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change in peak spacing, or selectivity. Separation selectivity depends on the mobile and stationary phases, temperature, the sample, and (to a much more limited extent) the column back pressure. The following discussion will emphasize the contribution of the stationary phase to selectivity (i.e., column selectivity) as a function of the sample components. When selecting a replacement column for a routine RPC method, an equivalent selectivity is usually necessary. In most cases, this can be achieved by the use of a column of the same kind or part number (e.g., different Sunfire C18 columns). There is some risk, however, that a column of the same part number may not always be available or have the same selectivity. It may then be necessary to locate a different column that can provide the same selectivity as the original column (an “equivalent” column; see Section 7.4.2). Alternatively, a column of quite different selectivity may be required during method development for various reasons (an “orthogonal” column; see Section 7.4.3). In either case, the nature of the sample can affect the relative similarity or difference in column selectivity. Soon after the introduction of C18 columns in the 1970s, it was found that relative retention can vary significantly among columns from different suppliers and even for nominally equivalent columns from the same source. This led to an ongoing interest in test procedures that can measure column selectivity [1–24]. The past four decades have seen numerous improvements in column manufacture (e.g., [25]), so columns of similar designation (same part number) are generally adequately reproducible [26–30]. Apart from the need to identify columns of either similar or different selectivity, there are other possible uses of test procedures for characterizing column selectivity. Thus, column selectivity arises from the different interactions that can take place between the sample and the stationary phase, and these same interactions determine other column-related phenomena of interest to the chromatographer. If column selectivity can be fully described in terms of such solute–column interactions, this information should prove more widely useful (as discussed in Section 7.4). This chapter describes one such characterization of column selectivity: the hydrophobic-subtraction model [31–52].

7.2  The Hydrophobic-Subtraction Model A number of different solute–column interactions can contribute to column selectivity: dipole–dipole, ion exchange, hydrogen bonding, π–π, etc. Some of these contributions to column selectivity (for neutral solute molecules) have been incorporated into the solvation equation, which describes an early model of RPC retention [53–55]: log k = C1 + rR2 + sπ 2H + aΣα 2H + bΣβ 2 + vVx

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separation conditions (i.e., mobile-phase composition and temperature). Solute properties are defined by R2, sπH2, ΣαH2, Σβ2 , and Vx (see the Symbols section for definitions). Terms ii, iii, and vi together determine the hydrophobic interaction between solute and column, term iv describes the effects of hydrogen bonding between acidic (donor) solutes and basic (acceptor) groups in the column, and term v represents the contribution of hydrogen bonding between basic solutes and acidic column groups. If the mobile phase and temperature are held constant, values of r, s, a, b, and v then partially characterize column selectivity. Equation 7.1 ignores contributions to retention from steric hindrance, ion exchange, and π–π complexation. While the model expressed by Equation 7.1 has many virtues (especially its applicability to a wide range of chromatographic and other phenomena), it is not sufficiently accurate for useful predictions of column selectivity or the accurate interpretation of solute–column interactions, and it cannot be used at all for ionized solutes.

7.2.1  Development of the Hydrophobic-Subtraction Model The development of the hydrophobic-subtraction (H-S) model began in 1998 with a review of the column-selectivity literature. Two extensive tabulations of RPC retention data [56,57] for a large number of different solutes and columns were of great value in this connection; a preliminary analysis of these values of k under the inspiration of Equation 7.1 helped guide subsequent experimental work and data interpretation. Earlier papers of the authors (especially Wilson et al. [31–33] and Gilroy, Dolan, and Snyder [34] and the review of Snyder, Dolan, and Carr [39]) describe the evolution of the H-S model over time. The remainder of this section will emphasize a unified picture of the model and its conceptual underpinnings, at the expense of peripheral details. Our experimental study began with the collection of retention factors k for 87 solutes of widely varied molecular structure [31,33], using nine different type-B alkylsilica columns. These initial experiments employed isocratic elution with 50% v/v acetonitrile/buffer at 35°C, and 30 mM potassium phosphate (pH 2.8) as buffer. Unless noted otherwise, the latter conditions can be assumed in the following discussion, as well as the use of type-B, monomeric alkylsilica stationary phases (for a description of type-B columns, see Sections 7.3.3.3 and 7.3.4.1). The day-to-day repeatability of experimental values of k was ±0.5% (1 SD), a precision that was anticipated (and found) to be necessary for the subsequent interpretation of these data. When values of log k for these 87 solutes were plotted for one RPC column versus another, approximately linear plots resulted. This is illustrated in Figure 7.2(a) for a Discovery C18 column versus an Agilent Eclipse XDB-C18 column. Linear plots as in Figure 7.2(a) suggest a single, dominant solute–stationary phase interaction, which we will refer to as hydrophobicity. Solute hydrophobicity can be defined by a quantity, η′, and column hydrophobicity by H1 and H2 (for columns 1 and 2, respectively). Values of log k for a given solute and columns 1 and 2 are then given by

(column 1)   log k1 = a + η′H1

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(a)

Figure 7.2  Linear plots of log k in RPC for one column (Discovery C18) versus another (Agilent Eclipse XDB-C18). (a) Data for 87 different solutes [31,33]; (b) expansion of enclosed region of (a). Separation conditions of Figure 7.1.

where a and b are constants. Linear-free-energy relationships of this kind are expected on theoretical grounds for various solute–column interactions, and they form the basis of Equation 7.1. Values of k for columns 1 and 2 (k1, k2) are therefore related as

log k1 = (a – b[H1/H2]) + (H1/H2) log k2



= C1 + C2 log k2

(7.3)

where C1 and C2 are constants for specified columns 1 and 2, with other conditions the same; thus, approximately linear plots of log k1 versus log k2 are expected. Note that what we refer to as “hydrophobicity” is collectively described by three different terms (ii, iii, vi) in Equation 7.1. Deviations from Equation 7.3 are of primary interest because these reflect solute–column interactions other than hydrophobic (and largely determine column selectivity). The region in Figure 7.2(a) enclosed by a dashed rectangle is expanded in Figure 7.2(b) so as to allow a better picture of deviations from the best-fit line through these data. The parallel lines (- - -) in Figure 7.2(b) correspond to an experimental repeatability of ±0.002 units (1 SD) in log k (i.e., ±0.5% in k). For several solutes in Figure 7.2(b), their deviations (δlog k) from the best-fit line exceed experimental error by factors of more than two. Assume next that the deviations δlog k for some solutes are determined primarily by a single solute–column interaction other than hydrophobicity. For example, fully protonated bases BH+ can interact strongly with ionized silanols –SiO – via cation exchange. The contribution of a given interaction to retention can be approximated by a product of some property of the solute (in this example, its effective charge κ′  ≈  +1) and some property of the column (which we will refer to as its cationexchange capacity C), so that for protonated solutes

δlog k ≈ κ′C

(7.4)

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For solutes i and j that each obey Equation 7.4, their values of δlog k for a different columns (with different values of C) will be related as

δlog ki = (κi/κj)δlog kj

(7.4a)

For two such solutes i and j, (κi  / κj ) will be constant and therefore plots of δlog ki versus δlog kj for different columns should be linear with zero intercept. The extent to which a plot of the form of Equation 7.4(a) is true for two solutes i and j (i.e., values of δlog k based on a single, common solute–column interaction) can be assessed by the linearity of plots of δlog ki versus δlog kj as measured by the coefficient of determination r 2. In our initial studies, values of r 2 ≈ 1.0 were found for various pairs of 25 structurally related solute pairs (out of 87 solutes studied)—for example, solute numbers 1/2, 3/4, 5/6, and 7/8 in Figure 7.3, as illustrated in the plots of Figure 7.4(a–d) for the latter solute pairs and nine different columns. All highly correlated solvent pairs could be assigned to one of four different groups: ii–v of Table 7.1. Each of these four solute groups appears to represent a different solute–column interaction (other than hydrophobic), tentatively identified (Section 7.3) as steric interaction (ii) hydrogen bonding between a basic solute and acidic column group (iii) or between an acidic solute and basic column group (iv) cation exchange or ion–ion interaction (v) The effects of hydrophobic interaction (i) exist for all solutes. Plots of δlog k for some solute pairs from different groups in Table 7.1 are shown in Figure 7.4(e–h), with

O2N

O O

CH2 NH C

O

O

(CH3CH2)2NC

H

O CH3

O 2-nitrobiphenyl (#1)

Fluorescamine (#2)

N-benzyl-formamide (#3)

Group ii

Group iii + H3C H N CH3

OH O N

N,N-diethylacetamide (#4)

O

CI

CH3

CH3 H3C

O

O

N+ H O

OH

OH

CI diclofenac acid (#5)

ketoprofen (#6)

Group iv

diphenhydramine (#7)

propranolol (#8)

Group v (pH-2.8)

Figure 7.3  Examples of solute pairs whose δlog k values are highly correlated. Solutes 1, 2: group ii; solutes 3, 4: group iii; solutes 5, 6: group iv; solutes 7, 8: group v. See text for details. © 2012 Taylor & Francis Group, LLC

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Figure 7.4  Examples of plots of δlog k versus δlog k for the solutes of Figure 7.3. Each plot represents data for nine type-B C18 columns described in references 31 and 33. Correlating solute pairs are (a) solute 1 versus solute 2; (b) solute 3 versus solute 4; (c) solute 5 versus solute 6; (d) solute 7 versus solute 8. Noncorrelating solute pairs are (e) solute 1 versus solute 3; (f) solute 4 versus solute 6; (g) solute 5 versus solute 8; (h) solute 1 versus solute 7. See text for details.

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Table 7.1 Grouping of Solutes According to Different Solute–Column Interactions Group

Nature of Solute

r2 a

n b

Proposed Interactions (See Equation 7.5) Columnd

Solutec i ii iii iv v

All solutes “Bulky” molecules Alkyl amides Non-ionized carboxylic acids Protonated bases

(0.99)e 0.97 0.92 0.88 0.99

87 12 2 6

η′ (hydrophobicity) σ′ (steric hindrance) β′ (H-B basicity) α′ (H-B acidity)

H (hydrophobicity) S* (steric hindrance) A (H-B acidity) B (H-B basicity)

5

κ′ (solute ionization)f

C (column ionization) f

Sources: L. R. Snyder et al. 2004. Journal of Chromatography A 1060:77; P. W. Carr et al. 2011. Journal of Chromatography A 1218:1724–1742. a Coefficient of determination from plots of δlog k for different solutes in a “similar” group. b n is the number of solutes in a group. c Symbol for solute property that determines the interaction in question. d Symbol for column property that determines the interaction in question. e Correlation of log k values for all solutes. f κ′ refers to the net charge on the solute molecule (e.g., +1 for a protonated base) and C refers to the negative charge on the stationary phase (e.g., positive for ionized silanols)

resulting poorer correlations (0.14 ≤ r 2 ≤ 0.36). For further details on the summary of Table 7.1, see reference 39. The retention of most solutes will be determined by two or more solute–column interactions, including hydrophobicity. If these various interactions are additive (as widely assumed, e.g., Equation 7.1 and reference 54), retention for all solutes should be given by an equation of the following form:

log k = log kEB + η′H – σ′S* + β′A + α′B + κ′C



(i)     (ii)    (iii)   (iv)   (v)



(7.5)

which recognizes possible contributions to k from all five interactions (i–v) of Table 7.1. The quantities η′, σ′, β′, α′, and κ′ of Equation 7.5 correspond to properties of the solute, while H, S*, A, B, and C represent complementary properties of the column or stationary phase (see Table 7.1). The quantity kEB refers to the value of k for ethylbenzene and corrects for differences in phase ratio. For type-B alkylsilica columns, Equation 7.5 describes values of k with an accuracy of about ±1% (2,700 values of k for 150 different solutes and 90 different columns [31,33,34]). For an average type-B C18 column from our original study, H will have a value of ~1.00 and values of S*, A, B, and C will be close to zero. Note that larger values of σ′S* mean increased steric resistance to penetration of the solute between the bonded chains, with a corresponding decrease in retention. As will be seen in Section 7.4, practical applications of the H-S model rely mainly on values of the column parameters H, S*, etc. Values of H correspond approximately © 2012 Taylor & Francis Group, LLC

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to the slope of plots as in Figure 7.2, where values of log k for the column of interest are plotted on the y-axis, and the x-axis now refers to average values of log k for nine different type-B C18 columns [31]. Values of the remaining column parameters (S*, A, B, C) were initially approximated by the average value of δlog k for the solutes in each of the four groups of Table 7.1 (for each of nine different columns). Beginning with the latter “trial” values of H, S*, etc. for each of these nine columns, the application of Equation 7.5 (multiple regression) to values of log k for 87 solutes and each column resulted in approximate values of the parameters η′, σ′, etc. for each solute. The regression was then repeated using values of log k and η′, σ′, etc. to derive revised values of H, S*, etc., and this process was continued until the standard error (SE) of the regression became constant (SE = ±0.004). Values of the parameters H, S*, etc. for other columns can be measured by a simpler version of the preceding approach; see Section 7.2.3. Resulting values of both the solute and column parameters are relative; it is only their products (η′H, σ′S*, etc.) that can be equated with an increment (δlog k) to values of log k (or the free energy of retention). For this and other reasons, it is necessary to weight values of H, S*, etc. when using these parameters to compare columns in terms of selectivity (Section 7.4.1). For type-B alkylsilica columns, Equation 7.5 has an accuracy of about 1% for predicted values of k. For other types of RPC column (e.g., phenyl, cyano), Equation 7.5 is generally less accurate (Section 7.3.7).

7.2.2  Effect of Separation Conditions on Column Selectivity A change in the mobile phase (organic solvent B and its concentration %B, buffer type and concentration, pH) or temperature can change values of k and affect the use of Equation 7.5 [32]. The results of such changes in conditions might be expressed as changes in either the solute or column parameters (or both). We have adopted the convention that solute parameters change with mobile-phase composition and temperature, but column parameters do not; this then allows the use of the same column parameters for different separation conditions, when a different column of either similar or different selectivity is chosen (as in Sections 7.4.1–7.4.3). The one exception is for the case of column ionexchange capacity C, which is known to vary with pH [58,59] and buffer concentration (Section 7.3.4). Thus, C represents the relative ionic charge of the stationary phase (its cation-exchange capacity), which is primarily determined by ionized silanols (Section 7.3.4). Silanol ionization increases with mobile-phase pH, as therefore do values of C. Similarly, buffer concentration also will affect ion-exchange retention and value of C. Given a value of C at pH 2.8 (C-2.8) from the application of Equation 7.5 to values of k for a given column, values of C at some other pH = x (i.e., C-x) can be determined from the change in retention of a quaternary ammonium compound (berberine, whose ionization does not change with pH):

C-x = C-2.8 + log (k x/k2.8)

(7.6)

where k x and k2.8 refer to values of k for berberine at pH x and pH 2.8, respectively. Values of C at pH x (C-x) are routinely derived for pH 7.0 to give values of C-7.0. Values of C for other pH values can then be estimated by interpolation between © 2012 Taylor & Francis Group, LLC

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pH 2.8 and 7.0. For 2.8 ≤ pH ≤ 7.0, values of H, S*, A, and B are unaffected by pH, while values of A begin to increase for pH > 7 (unreported data). Apart from pH and buffer concentration, we will assume that column selectivity does not change with separation conditions. Some consequences of this assumption will be explored in Section 7.4.1.

7.2.3  Routine Measurement of Column Selectivity The development of Equation 7.5 was described previously, based on the use of a mobile phase of 50% ACN/pH 2.8 buffer at 35°C. A similar procedure can be used to measure values of H, S*, etc. for any column (see Appendix 7.1 for details). Thus, given some minimum number of appropriate solutes, values of log (k/kEB) for these same solutes can be regressed against their values of η′, σ′, etc. to yield values of H, S*, A, B, and C-2.8. for the new column. A value of C-7.0 can then be measured by means of Equation 7.6. In practice, it has been found that 16 test solutes suffice for this purpose [34,37], which allows as many as six columns to be tested during an 8 h period. The number of required solutes can be reduced, but with some sacrifice in accuracy and precision (see the related discussion of Snyder et al. [37]). Some random examples of values of H, S*, etc. for different columns are shown in Table 7.2. Average values of H, S*, etc. for different column types are Table 7.2 Characterization of Column Selectivity by Means of the HydrophobicSubtraction Model (Equation 7.5)a Different C Columns

H

S*

A

B

C (pH 2.8)

C (pH 7.0)

kEB

(a) Different Column Types (Average Values) C1 (type B) C3 (type B) C8 (type B) C18 (type B) C18 (type B, wide pore) C18 (type B, monolith) C18 (type B, hybrid) C18 (polar end-capped) C18 (type A) C30 (type B) Embedded polar group Phenyl (type B) Cyano (type B) Perfluorophenyl (PFP) Fluoroalkyl Zirconia base

0.41 0.60 0.84 0.99 0.95 1.01 0.98 0.90 0.94 1.05 0.74 0.63 0.43 0.65 0.66 0.97

–0.08 –0.12 0.00 0.01 0.01 0.02 0.01 –0.04 –0.05 –0.01 0.00 –0.12 –0.09 –0.11 –0.07 0.01

–0.08 –0.08 –0.12 –0.01 –0.05 0.12 –0.14 –0.02 0.14 0.09 –0.22 –0.20 –0.49 –0.25 –0.11 –0.62

0.02 0.04 0.02 0.00 0.01 –0.02 –0.01 0.02 0.01 –0.02 0.12 0.02 0.00 0.01 0.03 0.00

0.04 –0.08 –0.03 0.00 0.22 0.11 0.13 –0.02 0.79 –0.08 –0.27 0.13 0.02 0.40 0.87 2.01

0.66 0.81 0.25 0.24 0.31 0.31 0.05 0.40 1.18 0.45 0.53 0.68 0.72 0.96 1.18 2.01

1.2 2.8 5.4 8.8 3.2 3.2 6.3 7.4 6.4 13.0 5.9 2.7 1.0 4.3 3.7 0.8 (Continued)

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Table 7.2 (CONTINUED) Characterization of Column Selectivity by Means of the HydrophobicSubtraction Model (Equation 7.5)a Different C Columns

H

S*

A

B

C (pH 2.8)

C (pH 7.0)

kEB

(b) Different Narrow-Pore, Type-B Alkylsilica C18 Columns (Values for Individual Columns) ACE 5 C18i Alltima C18g Chromolithj Discovery C18l Gemini C18 110Ak Halo-C18b Hypersil GOLDm Hypurity C18m Inertsil ODS-3f Kromasil 100-5C18d Luna C18(2)k Nucleodur C18 Gravityh ProntoSIL 120-5 C18 SHe Sunfire C18n Symmetry C18n TSKgel ODS-100Zo Xterra MS C18n Zorbax Eclipse XDB-C18c Zorbax StableBond C18c

1.00 0.99 1.00 0.98 0.97 1.11 0.88 0.98 0.99 1.05 1.00 1.06 1.03 1.03 1.05 1.03 0.98 1.08 1.00

0.03 –0.01 0.03 0.03 –0.01 0.05 0.00 0.03 0.02 0.04 0.02 0.04 0.02 0.03 0.06 0.02 0.01 0.02 –0.03

–0.1 0.04 0.01 –0.13 0.03 0.01 –0.02 –0.09 –0.15 –0.07 –0.12 –0.1 –0.11 0.04 0.02 –0.13 –0.14 –0.06 0.26

–0.01 –0.01 –0.01 0.00 0.01 –0.05 0.04 0.00 –0.02 –0.02 –0.01 –0.02 –0.02 –0.01 –0.02 –0.03 –0.01 –0.03 0.00

0.14 0.09 0.10 0.18 –0.09 0.06 0.16 0.19 –0.47 0.04 –0.27 –0.08 0.11 –0.19 –0.30 –0.06 0.13 0.05 0.14

0.10 0.39 0.19 0.15 0.19 0.04 0.48 0.17 –0.33 –0.06 –0.17 0.32 0.40 –0.10 0.12 –0.16 0.05 0.09 1.04

7.9 11.5 3.1 4.8 8 6.1 3.9 5.6 10.9 12.5 9.6 11 8.7 9.9 9.8 11.6 6.3 9.1 7.6

Source: Data from D. H. Marchand, L. R. Snyder, and J. W. Dolan. 2008. Journal of Chromatography A 1191:2. http:/www.USP.org/USPNF/columns.html (USP data base) a All columns: 5 μm particles. b Advanced Materials Technology. c Agilent. d Akzo Nobel. e Bischoff. f GL Science. g Grace-Alltech. h Macherey Nagel. i ACT. j Merck. k Phenomenex. l Supelco. m Thermo/Hypersil. n Waters. o Tosoh Bioscience.

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shown in Table 7.2(a), while values for a few individual type-B C18 columns are shown in Table 7.2(b). The interlaboratory reproducibility of values of H, S*, etc. has been determined. Four different laboratories performed this column characterization test for identical, virgin columns from the same production batch; 44 different columns (different part numbers) were studied. The results of this study (reproducibility of values of H, S*, etc.) are summarized in the sixth column of Table 7.3 (“observed”). The practical effect of error in measured values of H, S*, etc. is summarized in the seventh column as error in values of a comparison function Fs (see discussion in Section 7.4.1). Suffice to say, the experimental repeatability of values of H, S*, etc. is adequate for the use of values of Fs. Finally, the observed variation of these column parameters among different lots of the same column is summarized in the last column of Table 7.3 (“lot to lot”). The effect of inadvertent changes in separation conditions on measured values of H, S*, etc. is also shown in Table 7.3 (columns 2–5). On the basis of these results, it is recommended that conditions be controlled within the following limits: temperature, 35°C ± 0.5°C; acetonitrile concentration, 50% ± 0.05%; pH, 2.8 ± 0.1 or (berberine only) 7.0 ± 0.1. When available, 150 × 4.6 mm columns packed with 5 µm particles are preferred, with a flow rate of 2.0 mL/min. For columns with different particle sizes and/or dimensions, a change in flow rate may be needed so that pressures > 3000 psi are avoided. Columns must be equilibrated with the pH 2.8 mobile phase Table 7.3 Error in the Routine Measurement of the Column Parameters H, S*, etc. (Type-B Alkylsilica Columns) as a Function of Experimental Conditions Column Parameter

H S* A B C-2.8 C-7.0

Effect on Column Parameter of Indicated Change in Conditions + 1˚Ca

+1% ACNa

+0.1 pH unita

+1 mM buffera

–0.003 –0.001 0.006 0.000 0.002

–0.018 –0.012 –0.003 –0.002 –0.021

0.000 0.001 –0.001 –0.003 0.004

0.000 0.000 0.000 –0.001 –0.01

Experimental Repeatability of Each Column Parameter Observedb ±0.003 ±0.001 ±0.022 ±0.001 ±0.010 ±0.019

Effect on F sc

Lot to lot d

0.0 0.3 0.7 0.1 0.8 1.6

0.007 0.005 0.020 0.001 0.022 0.038

Sources: Procedures of J. J. Gilroy et al. 2004. Journal of Chromatography A 1026:77; L. R. Snyder et al. 2004. Journal of Chromatography A 1057:49. a Determined from data of N. S. Wilson et al. 2002. Journal of Chromatography A 961:195. b Interlaboratory (L. R. Snyder et al. 2004. Journal of Chromatography A 1057:49); ±1 SD for type-B alkylsilica columns. c Effect of “observed” repeatability; see Section 7.4.1. d For 11 different type-B alkylsilica columns (±1 SD; unpublished data).

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for at least 10 h before testing (Section 7.4.10.1); complete equilibration with pH 7.0 mobile phase is achieved within 1 h. Further details on the routine measurement of values of H, S*, etc. are provided in Appendix 7.1. More than 500 different RPC columns have so far been tested by this procedure, in each case starting with a virgin column. The possible effect of column use on values of H, S*, etc. is discussed in Section 7.4.7.

7.2.4  Phenyl, Cyano, and Other Column Types The selectivity of various column types other than type-B alkylsilica is summarized in Table 7.2(a) and discussed further in Section 7.3. For the application of Equation 7.5 to type-B alkylsilica columns, the resulting average SE (±0.004 units in log k) does not much exceed the experimental repeatability of values of log k (±0.002). For other column types, however, average values of SE are generally larger. A discussion of these errors is provided in Section 7.3.7. Columns bonded with calixarenes (macrocyclic compounds similar to cyclodextrins) have been characterized by an adaptation of the H-S model [60]. For these columns, it was claimed that the steric interaction term σ′S* of Equation 7.5 should be divided into two terms: one for flexible solute molecules (e.g., biphenyl) and one for rigid molecules (e.g., naphthalene). Other changes in the calculation of solute and column parameters were instituted for various reasons. The accuracy of this modified model was fivefold poorer (±0.020 units in log k), despite the rederivation of solute parameters for the nine columns studied (a procedure that greatly reduces error in predictions of retention for other column types; see Section 7.3.7). For less accurate models, as in this case, we have a concern that derived parameters for solutes and/or columns may be less representative of the assumed solute–column interactions; any resulting conclusions of the kind discussed in Section 7.3 may therefore be compromised to some extent.

7.3  The Nature of Various Solute–Column Interactions Cartoon representations of the various solute–column interactions i–v of Table  7.1 and Equation 7.5 are shown in Figure  7.5(a–e). These assignments were initially suggested [33] by the dependence of values of η′, σ′, etc. on solute molecular structure, and of values of H, S*, etc. on column properties such as ligand length and concentration, pore diameter, and end-capping. Recent work [50–52] based on hundreds of different columns has expanded our understanding of the five interactions of Equation 7.5, as will be summarized in this section. Except when stated otherwise, type-B alkylsilica columns are assumed, although other column types will be discussed. The interactions in Figure  7.5(f–h) are believed to occur for phenyl or cyano columns only and are discussed separately in Section 7.3.6. To the extent that the H-S model rests on a sound physicochemical basis, values of derived solute and column parameters represent quantitative measures of specific solute–column interactions. If this should prove to be the case, Equation 7.5 might prove applicable to a broad range of phenomena of interest to chromatographers © 2012 Taylor & Francis Group, LLC

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COCH 3

O

O

Hydrophobic interaction (d’H) (a)

O

O

Steric interaction (m’S*) (b)

O

C

OH

..N O

HO

O

..

O

Hydrogen bonding (_’B) (acidic solute) (d)

2

-

O

O

Cation exchange (g’C) (e)

Dipole-dipole interaction (cyano columns) (f)

NO2 O2N

+ C+ =N

O

-

NH + O

O

X

N

Hydrogen bonding (`’A) (basic solute) (c)

O

O

NO2

C=

N

O2N

O

O

/-/ interaction (phenyl columns)

/-/ interaction (cyano columns)

(g)

(h)

Figure 7.5  Cartoon examples of different solute–column interactions (≡Si-O-Si[CH3]2– shown as –O –).

(Section 7.4). Further tests of Equation 7.5 and a deeper understanding of these interactions are therefore important and, we hope, justify the following detailed discussion. Unfortunately, the complexity of RPC retention has in several instances required speculation on our part, and several puzzling observations remain to be explained satisfactorily. © 2012 Taylor & Francis Group, LLC

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7.3.1  Hydrophobic Interaction η′H Term i of Equation 7.5 (η′H, hydrophobicity) represents the major contribution to RPC retention. As illustrated in Figure 7.5(a), there is an attraction of less polar parts of the solute molecule for the nonpolar ligand of the stationary phase. Values of η′ and H describe solute and column hydrophobicity, respectively. 7.3.1.1  Solute Hydrophobicity η′ In the absence of other (nonhydrophobic) contributions to retention, Equation 7.5 becomes log k = log kEB + η′H

or

η′ = –(log kEB /H) + (1/H) log k = a + b log k

(7.7)

where a and b are constant for a given column. For example, for a Symmetry C18 column and 67 solutes described in Wilson et al. [31], the regression of values of η′ versus log k gives η′ = –0.92 + 0.92 log k; r 2 = 0.996, SE = 0.05 (i.e., in agreement with the form of Equation 7.7). Other columns yield similar correlations, supporting the conclusion that values of η′ are highly correlated with values of log k. A common measure of compound hydrophobicity is the octanol–water partition coefficient Po/w [61]. RPC retention can often be described [62,63] by log k = c + d log Po/w



(7.8)

where c and d are constants for a given column and separation conditions. Comparing Equations 7.7 and 7.8, it appears that values of η′ correlate with values of log Po/w, suggesting a similarity of η′ and log Po/w. For 29 solutes for which values of both η′ [31] and Po/w [61] could be found,

η′ = –1.48 + 0.44 log Po/w (r 2 = 0.94; SE = 0.14)

(7.8a)

Values of Po/w can be predicted from compound structure [61], which therefore implies a similar understanding of values of η′ versus solute structure (Equation 7.8a). 7.3.1.2  Column Hydrophobicity H Values of H vary with column conditions: ligand length n (e.g., n = 18 for C18) and concentration CL (micromoles per square meter), pore diameter dpore (nanometers), and whether or not the column is end-capped. A recent study [50] has reported values of H, S*, etc. and column conditions for 167 type-B alkylsilica columns. © 2012 Taylor & Francis Group, LLC

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The dependence of H on these column properties was investigated by a regression based on the following empirical equation: H = a  +  b n + c n2  +  d dpore + e dpore2  +  f CL + g CL2  +  h EC





     

   

     

ligand          pore      

(7.9)

ligand         end

length         diameter      concentration   capping

Values of the various coefficients a, b,…h result from the regression. EC has a value of 1.0 if the column is end-capped, and zero if it is not end-capped; the value of h thus represents the quantitative effect on H of end-capping. For a summary and further discussion of the application of Equation 7.9 to experimental value of H, S*, etc., see Table 7.12 in Appendix 7.2). Equation 7.9 accounts for about 93% of the variance of values of H; the remaining 7% variance appears due to differences in the silica used to prepare the column packing, as well as other changes in the manufacturing process that can affect retention (as discussed in Appendix 7.2). A graphical representation of H versus column properties (resulting from Equation 7.9) is shown in Figure 7.6, where H is plotted versus n in Figure 7.6(a), versus dpore in Figure 7.6(b), and versus CL in Figure 7.6(c). The effect of end-capping on H is shown in Figure 7.6(d). The two dashed curves n = 14.2 CL = 3.3 µmoles/m2

H

H

1.0

1.0 0.9

0.8

0

10 20 30 Pore Diameter dpore (nm) (b)

dp = 15 nm CL = 3.3 µmoles/m2 0

10 20 Ligand Length n (a) End-capping (+0.03) (corrected for n, dp, or CL)

30

1.0 H

0.6

0.9 0.8

n = 14.2 dp = 15 nm 0

1 2 3 4 5 Ligand Concentration CL (µmoles/m2) (c)

(d)

Figure 7.6  Dependence of column hydrophobicity H on column properties. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (d) column end-capping [50]. Values of “other” column properties assumed equal to average values for all columns; predicted values of (a–c) assume end-capped columns. The vertical scale for (a–d) is the same in each case. See text for details. (Adapted from P. W. Carr et al. 2011. Journal of Chromatography A 1218:1724–1742.) © 2012 Taylor & Francis Group, LLC

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for each plot in Figure 7.6(a–c) provide an estimate of reliability or error (each of the latter plots results from the separate application of Equation 7.9 to two randomly selected column subsets that each comprise half of the original 167 columns). In Figure 7.6(a–c), the values of other column properties are assumed to be equal to their average values for all 167 columns (values noted in the figure), and the predicted plots of Figure 7.6(a–c) assume end-capped columns. The vertical scale for Figure 7.6(a–d) in each case is the same, allowing a visual comparison of the relative effect of each column property on H. Larger values of H imply increased contact between column ligands and hydrophobic portions of the retained solute. An increase in H with increased ligand concentration is therefore expected and observed (Figure  7.6c). Likewise, a decrease in pore diameter with corresponding increase in the curvature of the (cylindrical) pore leads to increased crowding of the ligand ends, again with an increase in solute–ligand contacts and H (Figure 7.6b). For large enough pores, ligand crowding must eventually become unimportant, with a leveling of the plot of H versus dpore as observed. An increase in ligand length (Figure 7.6a) should (and does) increase H by increasing the probability of solute–ligand contacts. However, the slight decrease in H for n > 20 must represent some additional contribution of n to H. End-capping involves only a minor increase in column carbon content and is therefore expected (and found) to provide a relatively small increase in H (Figure 7.6d). 7.3.1.3  Values of H for Other Columns Values of H are generally lower for other column types (e.g., phenyl, cyano), as expected for these generally more polar ligands. This can be seen in Table 7.2(a) for different ligands of similar size. For example, a “phenyl” column (i.e., propylphenyl) has H ≈ 0.63, while a type-B C8 column has H ≈ 0.84. Similarly, a “cyano” column (i.e., –C3C≡N) has H ≈ 0.43, versus a value of H ≈ 0.7 for a type-B C5 column. Because H represents the dominant contribution of the column to solute retention and type-B alkylsilica columns generally have higher values of H (Table 7.2), other columns tend to exhibit generally weaker retention, which in turn may require a weaker mobile phase for adequate values of k.

7.3.2  Steric Interaction σ′S* In size-exclusion chromatography (SEC), larger molecules are restricted from entering particle pores that are smaller than the solute molecule, so solutes do not penetrate the pores of the particle and are therefore less retained. As a consequence, large molecules leave the column earlier, and retention is determined by solute molecular size. In similar fashion, steric interaction can be visualized as partial exclusion (or restricted retention) of solute molecules from the spaces between stationary-phase ligands. While retention in SEC is related to the ability of a solute to penetrate the pores of the particle, steric interaction describes the ability of the solute to penetrate the stationary phase. In both SEC and steric interaction, molecular “size” is determined by the length of the solute molecule (its hydrodynamic or “Stokes” diameter). Longer molecules require more space to “move around” and their entropy is decreased when confined to a smaller space—thereby decreasing their retention. © 2012 Taylor & Francis Group, LLC

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Another kind of steric hindrance in RPC is referred to as shape selectivity [64– 69]. Evidence presented later suggests that steric interaction and shape selectivity are distinctly different phenomena. Shape selectivity occurs for more “congested” stationary phases, where insertion of a “bulky” solute molecule requires the presence or formation of a large enough cavity to accept the solute. Steric interaction in Equation 7.5 is described by term ii (σ′S*), where σ′ refers to solute “bulkiness” and S* refers to the relative resistance of the stationary phase to entry of a “bulky” molecule. The proposed basis of steric interaction is illustrated in Figure 7.5(b) and described in more detail later. As noted in Table 7.1, 12 solutes of the original 87 exhibit predominant steric interaction, with an average δlog k correlation of r 2 = 0.97. That is, the σ′S* term of Equation 7.5 very likely represents a single, distinct interaction. The following account of steric interaction and its comparison with shape selectivity is drawn mainly from Carr et al. [50]. 7.3.2.1  Solute Bulkiness σ′ Values of σ′ are determined mainly by solute length L, where L can be approximated by the number of atoms (other than hydrogen) in a line from one end of the molecule to the other (without doubling back); see reference 33 for details). For example, ethylacetate CH3C

O O CH2CH3 L=5

benzene CH

CH CH CH CH L=4

CH

nitrobenzene CH

CH CH CH CH

CN

O O

L=6

The dependence of σ′ on L is illustrated in Figure  7.7 for solutes that do not exhibit attractive, nonhydrophobic interactions with the stationary phase; that is, solutes for which terms iii–v of Equation 7.5 are negligible. The particular solutes in Figure 7.7 include (a) hydrocarbons and (b) solutes whose correlating values of δlog k place the solute in group ii of Table 7.1 (with r 2 ≥ 0.90). A reasonable correlation is observed in Figure 7.7:

σ′ = –1.46 + 0.32 L – 0.01 L2   (r 2 = 0.88)

(7.10)

for the latter solutes, as well as for a majority of other solutes for which we have values of σ′ [50]. Solutes that deviate significantly from the relationship of Figure 7.7 usually have values of σ′ that are smaller than predicted. Deviating solutes also tend to interact with the stationary phase by hydrogen bonding or ion exchange. Such an interaction tends to “localize” the molecule in a specific orientation within the stationary phase; this means a restriction of the molecule′s movement within the stationary phase. This should in turn result in smaller values of σ′ versus predictions by Equation 7.10 because restricted molecules will be less likely to differentiate between columns with different S* values (see later discussion). Retention as a result of shape selectivity is greater for planar versus nonplanar molecules, but this effect is smaller for steric interaction. Molecules with © 2012 Taylor & Francis Group, LLC

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1.0

σ´

0.5

0.0

–0.5

Hydrocarbons r 2 ≥ 0.90 0

5

10 Solute Length L

15

Figure 7.7  Correlation of solute bulkiness σ′versus column length for solutes that exhibit only hydrophobic or steric interaction with the column [50]. These solutes are either hydrocarbons (e.g., benzene, toluene, naphthalene) that are not substituted by polar groups or solutes in group ii of Table 7.1 that are highly correlated (r 2 ≥ 0.90). See text for details. (Adapted from P. W. Carr et al. 2011. Journal of Chromatography A 1218:1724–1742.)

larger length-to-width (L/W) values are also preferentially retained by shape selectivity, which is the reverse of the case for steric interaction (longer molecules less retained). 7.3.2.2  Column Steric Resistance S* Values of S* can be correlated with column properties by means of Equation 7.9, with S* replacing H [50]. The latter relationship accounts for about 78% of the variance of values of S*; as in the case of H, the remaining variance appears largely due to differences in the silica and other changes in the manufacturing process (Appendix 7.2). Plots of S* versus column properties are shown in Figure 7.8, just as for H in Figure  7.6 (dashed curves again represent an estimate of the uncertainty in these plots). As in Figure 7.6, the values of other column properties are assumed equal to their average values for all 167 columns, and the predicted values of Figure 7.8(a–c) assume end-capped columns. The vertical scale for Figure 7.8(a–d) is in each case the same (but different from that in Figure 7.6), allowing a visual comparison of the relative effect of each column property on S*. S* initially increases with ligand length (Figure 7.8a), reaches a maximum value for n ≈ 15, and then undergoes a steep decrease for larger values of n (Figure 7.8a). Since the value of S* is similar for both C1 and C30 columns and there can be little steric interaction for a C1 column, it appears that there is at most a small effect of steric interaction for C30 columns. For monomeric columns as in Figure  7.8, the dependence of shape selectivity ϕSS = log(1/αTBN/BaP) on n is quite different (Figure 7.9a); here, αTNN/BaP is the ratio of values of k for tetranaphthonaphthalene and benzo[a]pyrene [50]. Values of ϕSS are constant (and presumed minimal) for n ≤ 18 and then increase sharply for n = 30. © 2012 Taylor & Francis Group, LLC

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S*

0.04

0.06

0.02

0.04

0.00

0.02

–0.02

S*

–0.04 –0.06

0

10 20 Ligand Length n

30

(a)

–0.02 –0.04 –0.06 –0.08

0.04 S* 0.02 0.00

0.00

5 0 1 2 3 4 Ligand Concentration CL (µmoles/m2) (c)

0

10 20 30 Pore Diameter dpore (nm) (b)

End-capping (+0.07) (corrected for n, dp, or CL) (d)

Figure 7.8  Dependence of column steric resistance S* on column properties [50]. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (c) pore diameter dpore; (d) column end-capping. See Figure 7.6 caption and discussion for other details. (Adapted from P. W. Carr et al. 2011. Journal of Chromatography A 1218:1724–1742.)

The dependence of S* on ligand length has been rationalized as follows. For n = 1, solute molecules adsorb onto the stationary phase surface, without significant penetration into the stationary phase [70]. There is therefore little steric interaction and resulting small values of S*. As n increases, there is increasing penetration of the solute into the stationary phase and correspondingly larger values of S* as the solute molecule becomes more restricted by the surrounding stationary phase. For n > 15, however, solute penetration becomes complete and restricted retention levels off, while the interligand volume continues to increase, allowing more freedom of movement for molecules that are held within the stationary phase. For large enough values of n (e.g., n = 30), the latter effect predominates, steric interaction becomes less important, and values of S* become smaller. Values of S* decrease with increasing pore diameter (Figure 7.8b), but the effect is relatively small. As with the dependence of H versus dpore, an increase of S* for smaller pores can be explained by the greater crowding of ligand ends. Ligand concentration has a large effect on S* (Figure 7.8c), increasing steadily as CL increases. This is expected because an increase in CL will decrease the space between ligands that is available for the free movement of a retained solute. As seen in Figure 7.9(b), shape selectivity ϕSS also increases for higher concentrations of the ligand, especially for polymeric columns and CL > 4. In contrast to steric interaction and values of S*, shape selectivity increases for wider pores [65]. © 2012 Taylor & Francis Group, LLC

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ΦSS

0.2 0.0 –0.2

Monomeric 0

5

10

15 20 Ligand Length n

25

30

Shape selectiviy

(a) 0.8

Monomeric Polymeric

ΦSS

0.4 0.0 –0.4 –0.8

0

2 4 6 Ligand Concentration CL (µmoles/m2)

8

(b)

Figure 7.9  Variation of shape selectivity ΦSS (equal to –log [αTBN/BaP]) as a function of column properties. (a) Effect of ligand length n; (b) effect of ligand concentration CL . “Monomeric” and “polymeric” refer to the nature of the stationary phase (see Chapter 5 in reference 72). Values of ϕSS derived from values of αTBN/BaP are reported in references 63 and 68. See text for details. (Adapted from P. W. Carr et al. 2011. Journal of Chromatography A 1218:1724–1742.)

End-capping (Figure 7.8d) increases values of S* by 0.07 units, an effect that is relatively much greater than the effect of end-capping on H (Figure 7.6). While this is a surprising result, other evidence confirms the relative importance of end-capping on S* [50]. It has been speculated that end-capping reduces the amount of water and organic solvent held near the substrate surface of the stationary phase, which in turn reduces ligand flexibility and the number of favorable configurations available to the solute. The result should be an increase in S* (as observed). End-capping has no effect on shape selectivity [65]. Several column properties are seen to affect steric interaction and shape selectivity quite differently. It is also found that values of S* do not correlate with a common measure of shape selectivity (αTBN/BaP). It thus appears that shape selectivity and steric interaction describe two different phenomena. While both steric interaction and shape selectivity reflect steric hindrance in the stationary phase, steric interaction is consistent with a decrease in entropy for retained “bulky” molecules; shape © 2012 Taylor & Francis Group, LLC

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selectivity appears to be primarily an enthalpic process that may require the creation of spaces within the stationary phase for bulky solute molecules. 7.3.2.3  Values of S* for Other Columns The preceding discussion applies just for type-B alkylsilica columns, with average values of S* = 0.00 ± 0.05. Similar values of S* are found [47] for embedded polar group columns (0.00 ± 0.06), but not for cyano (–0.09 ± 0.03), phenyl (–0.12 ± 0.06), hexylphenyl (–0.09 ± 0.05), or pentafluorophenyl (–0.11 ± 0.04) columns—all of which have lower values of S* (even when differences in ligand length are taken into account [50]). Euerby has noted a greater shape selectivity for PFP columns, based on the relative retention of triphenylene versus o-terphenyl (αT/O) [73]. However, cyano and phenyl columns are capable of π–π interaction (Section 7.3.6) with aromatic solutes [40–42], while values of αT/O are derived from the retention of aromatic solutes (triphenylene and o-terphenyl) whose π–π interactions with a phenyl (or cyano) column are likely to differ. This casts doubt on the use of values of αT/O as indicators of steric hindrance for cyano or phenyl columns. A similar argument might be raised for values of S* because the latter values are determined mainly by two aromatic solutes (cis- and trans-chalcone), each of which is capable of π–π interaction. However, we do not believe that π–π interactions for the latter two solutes are likely to be much different from the other solutes used for the measurements of values of H, S*, etc. (Table 7.11 in Appendix 7.1). This is supported by the generally lower values of S* for phenyl and cyano columns.

7.3.3  Hydrogen Bonding β′A Term iii of Equation 7.5 (β′A) is believed to arise from the hydrogen-bond (H-B) interaction between a column silanol (–SiOH) and an acceptor group in the solute molecule (e.g., the ≡N: group of pyridine in Figure 7.5c). Values of β′ and A describe solute H-B basicity and column H-B acidity, respectively. 7.3.3.1  Solute Hydrogen-Bond Basicity β′ Compound H-B basicity in solution can be described by the parameter β2 of Equation 7.1. When values of β′ (Equation 7.5) and β2 are compared for a diverse group of solutes, a generally poor correlation is found. This is illustrated for various amide solutes in Table 7.4. As the size of alkyl groups attached to the nitrogen increases, H-B basicity in solution (β2) increases slightly, while values of β′ decrease sharply. This contrasting behavior can be attributed to a much greater effect of steric hindrance on hydrogen bonding in the more crowded stationary phase than in solution. This is further illustrated by the examples of Figure 7.10a for three homologous series substituted by different H-B acceptor groups. In each case (amides, alcohols, nitriles, respectively), values of β′ decrease with increase in the combined lengths of attached alkyl groups (measured in Figure 7.10a by the total number of attached alkyl carbons n′). Corresponding values of β2 are much less affected by n′ (as in Table 7.4 for amides). Steric hindrance is even greater for aromatic solutes, which should result in generally smaller values of β′. This is confirmed in Figure 7.10(b) for © 2012 Taylor & Francis Group, LLC

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Table 7.4 Values of Hydrogen-Bond Basicity in Solution (β2) and RPC (β′) for Various Amide Solutes Solute

n′a

β2b

β′c

N,N-dimethylformamide N,N-dimethylacetamide N,N-diethylformamide N,N-diethylacetamide N,N-dibutylformamide N-benzylformamide

2 2 4 4 8 7

0.74 0.78 0.76 0.78 0.80 0.63

0.89 0.99 0.49 0.53 0.20 0.10

a

b

c

Number of carbons in groups attached to the nitrogen of the amide group. H-B acceptor strength in solution (M. H. Abraham and J. H. Platts. 2001. Journal of Organic Chemistry 66:3484). Data of Table 7 in N. S. Wilson et al. 2002. Journal of Chromatography A 961:171.

the distribution of values of β′ for aromatic versus aliphatic solutes (aliphatic solutes have generally larger values of β′). In order to compare values of β′ with H-B basicity, the effects of steric hindrance must first be made comparable for each H-B acceptor group. For aliphatic solutes, this can be achieved by comparing solutes with similar steric hindrance (same values of n′). For example, a value of n′ = 4 can be assumed, as illustrated in Figure 7.10(a) (dashed vertical line at n′ = 4, corresponding to N,N-diethyl formamide, 1-butanol, and n-valeronitrile, respectively). Values of β′ for different solutes with n′ = 4 correlate reasonably well with values of β2 (r 2 = 0.85, [31]):

β′ = –0.47 + 1.34 β2  (SE = 0.09, n = 10)

(7.11)

confirming the dependence of values of β′ on solute H-B basicity. Aromatic compounds that are unsubstituted in the ortho position should exhibit similar steric hindrance (but greater hindrance than corresponding aliphatic solutes); a lesser (but significant) correlation (r 2 = 0.45) is found for these solutes:

β′ = –0.06 + 0.24 β2 (SE = 0.04, 11 solutes)

(7.11a)

The poorer correlation of Equation 7.11(a) versus Equation 7.11 is likely the result of smaller values of β′ for aromatic versus aliphatic solutes (as in Figure  7.10b) together with similar experimental error for values of β′. The greater steric hindrance of aromatic solutes is also demonstrated by the smaller β2 coefficient (0.24 in Equation 7.11a versus 1.34 for aliphatics in Equation 7.11), although electron © 2012 Taylor & Francis Group, LLC

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Figure 7.10  Solute H-B basicity β′. (a) Dependence on number of carbons (n′) attached to basic group; (b) distribution of values of β′ for aromatic and aliphatic solutes [52]. See text for details.

withdrawal by the phenyl group may be an additional contributor to lower values of β′. 7.3.3.2  Column Hydrogen-Bond Acidity A Values of A for 167 type-B alkylsilica columns can also be related to column properties by means of Equation 7.9, with A replacing H. The latter relationship accounts for about 69% of the variance of values of A; all but about 4% of the remaining variance appears due to differences in the silica and other changes in the manufacturing process (Appendix 7.2). Plots of A versus column properties are shown in Figure 7.11, just as for H in Figure 7.6. A increases with ligand length n, decreases with pore diameter dpore, increases with ligand concentration CL , and is decreased by end-capping. The relative importance of column conditions in affecting values of A varies as end-capping ≈ n > CL > dpore. © 2012 Taylor & Francis Group, LLC

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Lloyd R. Snyder, John W. Dolan, Daniel H. Marchand, and Peter W. Carr 0.2

0.0

0.1

A –0.1

0.0

–0.2

0

–0.1

(b)

–0.2

0.0

–0.3

–0.1 A

–0.4 –0.5

10 20 30 Pore Diameter dpore (nm)

0

10 20 Ligand Length n (a)

30

–0.2 –0.3 0

1 2 3 4 5 Ligand Concentration CL (µmoles/m2) (c)

(d ) End-capping (–0.32)

Figure 7.11  Dependence of column H-B acidity A on column properties [51]. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (d) column end-capping [51]. See discussion of Figure 7.6 for other details.

End-capping removes silanols (–SiOH), which are assumed to be responsible for the H-B interaction of acceptor solutes with the stationary phase (Figure  7.5c). A relatively large decrease in A as a result of end-capping is therefore both expected and observed (Figure 7.11d). An increase in ligand concentration CL should also lead to a decrease in sila­ nols and therefore a decrease in A. As seen in Figure 7.11(c), however, the opposite result is observed. It has been observed that end-capping with small silanes such as ClSi(CH3)3 allows a more complete reaction of silanols, versus the bonding reaction with large silanes such as ClSi(CH3)2C18 [72]. Because all the columns represented in Figure 7.11(a–c) are end-capped, it is conceivable that an increase in ligand concentration could result in an increase in unreacted silanols [51]. The observed increase in A for longer ligands (Figure 7.11a) can be compared with a decrease in A for wider pores (Figure 7.11b) and increase of A for higher ligand concentrations, which together suggest that A increases for more hydrophobic columns (those with larger values of H; see Figure 7.6), apart from the separate effect of silanols on A. This behavior is reminiscent of the “hydrophobically assisted ion-exchange interaction mechanism” described by Neue et al. [74], whereby ion-exchange and

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reversed-phase (i.e., hydrophobic) interactions cooperate for maximum retention. A similar enhancement of retention may exist for other polar interactions such as (in the present case) hydrogen bonding. While Equation 7.5 recognizes such combined interactions by separate η′H and β′A terms, there may be an additional synergistic effect of the two interactions that accounts for the apparent dependence of A on column hydrophobicity. 7.3.3.3  Values of A for Other Columns Compared to the type-B alkylsilica columns discussed before, other column types can have either higher or lower values of A. Higher values of A presumably reflect higher concentrations of more acidic silanols, while lower values might indicate either more effective shielding of silanols from interaction with the solute or a competitive interaction of stationary-phase ligands with silanols. Alkylsilica columns with C-2.8 > 0.3 can be classified as type A (see later discussion of Section 7.4.8). Type-A silica is contaminated with metals such as Al[III] and Fe[III] that are believed to create activated (more acidic) silanols, which should result in larger values of A. For 248 C18 columns for which we have data (as of the time this chapter was submitted), the average values of A are –0.05 ± 0.23 (type B) and +0.15 ± 0.17 (type A). The large standard deviation for each of these values reflects in part the presence of both end-capped and non-end-capped columns in each group, as well as variations in other column properties. Nevertheless, there is a strong tendency for type-A columns to have higher values of A, as expected. Type-B phenyl columns have an average value of A equal to –0.26 ± 0.14, which can be compared to the value (0.12 ± 0.15) for type-B C8 columns (i.e., similar ligand sizes). Presumably, the phenyl group shields silanols more effectively. Similarly, the average value of A for type-B cyano columns is –0.49 ± 0.18, which can be compared with the value for type-B C4 columns of similar ligand size (–0.23 ± 0.17). As in the case of phenyl columns, it appears that the cyano group interferes with the H-B interaction of solutes with silanols. Finally, values of A for embedded polar group (EPG) columns average –0.25 ± 0.37, which is somewhat lower than for type-B alkylsilica columns of similar ligand length (A ≈ –0.1). The polar group in EPG columns is usually a strong H-B acceptor, which might favor its interaction with silanols and result in lower values of A.

7.3.4  Cation Exchange κ′C For samples that contain ionized solutes, the column cation-exchange capacity C has the greatest effect on column selectivity [46]. Term v of Equation 7.5 (κ′C) has been attributed to the ion exchange of a cationic solute (e.g., a protonated base BH+ as in Figure 7.5e) with a buffer cation (e.g., K+) held by an ionized silanol (–Si-O –):

BH+ + –SiO– K+ ⇔ –SiO– BH+ + K+

(7.12)

The κ′C term of Equation 7.5 may also include other interactions between ionized solutes and stationary phases, as will be seen.

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log k

0.0

0.0

Inertsil ODS-3 C-2.8 = –0.47

–0.5

StableBond 300Å C18 C-2.8 = 0.25

–0.5 –1.0 –1.0 –1.0

–0.5 (a)

0.0 log k (avg.)

–1.0

–0.5

0.0

(b)

Figure 7.12  Partial plots as in Figure 7.2(b) of log k for 87 different solutes and two different columns (noted in the figure). The y-axis corresponds to log k values for two selected columns, Inertsil ODS-3 (a) and StableBond (b) that have quite different values of C-2.8. The x-axis corresponds to average values of log k for nine different columns that include the Inertsil and StableBond columns. Five fully protonated, strong bases are shown as •. See text for details.

The importance of ionic interactions for type-B alkylsilica columns at low pH has been questioned [75], and the retention of ionized bases has instead been attributed to ion-pair formation (see later discussion). However, for phosphate as buffer this is contradicted by the example of Figure 7.12 for a mobile-phase pH of 2.8. Five fully protonated strong bases (shown as •) are seen to be preferentially retained by the StableBond 300Å C18 column (Figure 7.12b), compared to the Inertsil ODS-3 column (Figure 7.12a). The x-axis represents average values of log k for nine different columns, while the y-axis corresponds to log k values for individual columns. Because only the column differs in the two plots of Figure 7.12(a, b) (i.e., same mobile phase and temperature) and the only common characteristic of these strong bases is their positive charge, it follows that the charge on the two columns must be different (a more negative column in Figure 7.12b, with a higher value of C-2.8). An understanding of the retention of ionizable compounds will be seen to be somewhat complicated. Some background information will therefore be necessary before examining values of κ′ and C as functions of the sample and column, respectively. 7.3.4.1  Stationary-Phase Charge Silanols can ionize at higher pH (–SiOH ⇔ –SiO – + H+), as has long been recognized [76]. The extent of silanol ionization in RPC columns varies with both mobile-phase pH and silica type and can be estimated from the ion-exchange retention of an inorganic cation such as Li+ [77,78]. This is illustrated in Figure 7.13 for three different C18 columns, for each of which the retention of Li+ (by ion exchange) is plotted versus mobile-phase pH. The greater Li+ retention (and implied silanol ionization) for the Resolve C18 packing results from the use of an older type-A silica with more acidic silanols. The hybrid column of Figure 7.13 is the least acidic. In addition to ionized silanols, it has been shown [79,80] that some columns contain positively charged groups (with a concentration q+) that are believed to arise from contaminants introduced during stationary-phase manufacture. It has been further shown © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 325 20 Resolve C18 (type-A)

tR (Li+)

15 10

Symmetry C18 (type-B)

5

Increasing silanol ionization and cationexchange capacity

Hybrid C18 3

4

5

6

pH

7

8

9

10

Figure 7.13  Ion-exchange capacity of different C18 columns as a function of pH, as measured by the retention time tR of Li+. (Adapted from A. Mendez et al. 2003. Journal of Chromatography A 986:33.)

[47] that values of q+ tend to be greater for columns with more negative values of C-2.8 (Figure 7.14a), suggesting that values of C-2.8 might be determined (at least in part) by values of q+. As seen in Figure 7.14(b), the majority of type-B alkylsilica columns appear to be free of any positive charge. Whereas the negative charge q– on a column increases with mobile-phase pH, the positive charge q + decreases [80]. An important question is whether the charge on a column (q– or q+) as measured by the retention of an inorganic ion (Li+ or NO –3) plays a comparable role for the retention of larger organic ions such as berberine. A value of q+ for a given column is calculated from (and is proportional to) the slope c(NO –3) of a plot of k for NO –3 versus 1/(buffer concentration) [79]. Values of c(NO –3) ∝ q+ for NO –3 are highly correlated with corresponding values of c(TS–) ∝ q+ for toluene sulfonate (TS–):

c(TS–) = 1.93 c(NO –3) (r 2 = 0.997, n = 12)

(7.13)

suggesting that the retention of both NO –3 and organic anions, such as toluene sulfonate, responds to values of q+ in the same way (i.e., both solutes can undergo anion exchange with the same positive groups within the stationary phase). However, it seems less likely that values of q – (measured by the retention time of Li+) will correlate as well with the cation exchange of organic molecules. Thus, Figure 7.13 suggests an absence of cation exchange for the hybrid C18 column when pH < 9, whereas for a different hybrid column (XTerra RP-18), k for berberine increases by more than twofold for an increase in pH from 2.7 to 9 [81]. 7.3.4.2  Different Retention Processes for Cationic Solutes The data of Figure 7.13 suggest that silanol ionization and cation exchange as in Equation 7.12 may be negligible for type-B alkylsilica columns when the mobilephase pH is 0, Figure  7.14(a) shows increasingly negative values of q +. This indicates an increasing repulsion of NO –3 from the stationary phase for columns with C-2.8 > 0, in turn implying an increasing (net) negative charge on the column. Finally, as shown later, values of C-2.8 < 0 do not correlate with column properties, implying the presence of two different ionic groups within the stationary phase. A similar plot for an anionic solute (4-toluenesulfonate, TS –) is shown in Figure  7.16(d). Anion exchange can occur for C-2.8 ≤ 0 (negative values of d, Equation 7.16) because of a significant positive charge on the column q+ (Figure  7.14a). Likewise, positive values of d for C-2.8 ≥ 0 suggest RPC retention (Equation 7.14) with shielding of the solute TS – from a negative charge on the column by adjacent buffer anions (or ion pairing with the buffer cation K+). As a result, values of d approach the theoretical limit of d = –1 for C-2.8 < –0.5, while exhibiting positive values for C-2.8 > 0.1. It is tempting to conclude from Figure 7.16(c, d) that columns with C-2.8 < 0.1 are predominantly positive at low pH, while columns with C-2.8 > 0.1 are predominantly negative (as supported by Figure 7.14a). 7.3.4.4  Peak Tailing and Cation Exchange To further clarify the preceding questions concerning cation exchange at low pH and the related possibility of negatively charged groups in the stationary phase, other kinds of information are needed. Preliminary data [51] suggest that peak tailing increases © 2012 Taylor & Francis Group, LLC

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with the extent of cation exchange (as opposed to other retention processes), in turn allowing the extent of cation exchange to be inferred from the degree of peak tailing. For the experiments of Figure 7.16(c), where for different columns at pH 3 there is a continuing decrease in the slope d of plots of log k versus log M, peak tailing as measured by the asymmetry function As [72] varies with column C-2.8 values as

(2.4 mM buffer) As = 3.5 + 4.4 C-2.8 (r 2 = 0.71, n = 12)

(7.17a)



(9.8 mM buffer) As = 2.6 + 2.8 C-2.8 (r 2 = 0.50, n = 12)

(7.17b)

These results (weakly) suggest that cation exchange (as measured by values of As) increases with column acidity C-2.8 (i.e., cation exchange appears to exist for these columns at pH 3). Note that the coefficient of C-2.8 in Equations 7.17(a) and 7.17(b) is larger (4.4 versus 2.8) for the weaker buffer (2.4 mM), as expected for the greater suppression of cation exchange by a stronger buffer (9.8 mM). See [51] for further details that were unavailable at the time this chapter was submitted. 7.3.4.5  Solute Ionic Charge κ' The distribution of values of κ′ at pH 2.8 for 87 different solutes is summarized in Figure 7.17. Benzoic acids and anilines that are ionized significantly (>10%; [32]) are noted in the figure; the strong bases of Figure 7.19 are ~100% ionized. The average value of κ′ for the strong bases is 1.0 ± 0.2 (i.e., the value of κ′ is approximately equal to the charge (+1) on these molecules). In the case of the partly ionized anilines, their average value of κ′ = 0.09 ± 0.00 is much smaller than the average charge on these molecules (+0.7 ±0.9) because the uncharged molecule is preferentially retained. For the ionized acids, the average value of κ′ (–0.3 ± 0.2) is closer to the average charge on the molecule (–0.5 ± 0.2), which would be predicted if these ionized acids are retained mainly by anion exchange. For neutral solutes, the average value of κ′ = –0.01 ± 0.02. Thus, values of κ′ are consistent with the extent of ionic interaction of the solute and column. It should be noted also that the hydrophobicity η′ of an ionizable solute will change with its ionization, as should be apparent from the derivation of Equation 7.5.

# of Solutes

40 30 Ionized anilines

20 10 –0.5

Ionized acids –0.3

Strong bases –0.1

0.1

0.3

κ´

0.5

0.7

0.9

1.1

1.3

Figure 7.17  Distribution of values of κ′ for 87 solutes [31,33]. Indicated solute types (acids, anilines, strong bases) are the only compounds that are significantly ionized (>10%). © 2012 Taylor & Francis Group, LLC

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Similarly, its value of κ′ will increase for bases (and decrease for acids) as they become more ionized. 7.3.4.6  Column Cation-Exchange Capacity C-7.0: Effect of Column Properties The application of Equation 7.9 (with C-7.0 replacing H) to 167 type-B alkylsilica columns resulted in a correlation of r 2 = 0.666. All but ~7% of the remaining variance appears due to differences in the silica and other changes in the manufacturing process (Appendix 7.2). Plots of C-7.0 versus column properties are shown in Figure 7.18, just as for H in Figure 7.6. Note the greater spread in the dashed curves that measure the reliability of these plots, corresponding to somewhat reduced confidence in these dependencies of C-7.0 on different column properties. This somewhat greater uncertainty in the plots of Figure 7.18 is likely a consequence of 0.3

0.8

0.2

C-7.0

0.9

0.7

0.0

0.5

0.3

0.2

0.2

0.1

0.1 0.0 –0.1

0

10 20 30 Pore Diameter dpore (nm) (b)

0.4

C-7.0

C-7.0

0.6

0.1

0.0 –0.1

0

10 20 Ligand Length n

30

0 1 2 3 4 5 Ligand Concentration CL (µmoles/m2) (c)

(a) End-capping (–0.67) (no correction for n, dp, or CL) (d)

Figure 7.18  Dependence of column cation-exchange capacity at pH 7.0 (C-7.0) on column properties. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (d) column end-capping. See discussion of Figure 7.6 for other details. (Adapted from D. M. Marchand et al. 2011. Journal of Chromatography A 1218:7110.) © 2012 Taylor & Francis Group, LLC

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the importance of silica ionization in affecting values of C-7.0 (not recognized in Equation 7.9), unlike the case for H, S*, or A in Figures 7.6, 7.8, and 7.11. The relative importance of the effects of each column property on C-7.0 varies as

End-capping > n > CL ≈ dpore

End-capping decreases values of C-7.0 by –0.67 units (Figure 7.18d)—a very large effect relative to that for other column properties. This is expected because the corresponding removal of silanols should reduce column ionization and values of C. Reasons for the dependence of C-2.8 on other column properties (Figure 7.18a–c) are less obvious. Values of C-7.0 appear to follow a parabolic dependence on ligand length n, with a general trend to higher values for larger n (possibly the result of the “multiplicative ion-exchange interaction” [74] cited in Section 7.3.3 for values of A versus column properties). There is a moderate decrease in C-7.0 with increasing ligand concentration C L (Figure 7.18c) and an increase for increasing pore size (Figure 7.18b). These trends are the opposite of those observed for values of A (Figure 7.11). The silanols relevant to these two column parameters are ionized in the case of C-7.0 and non-ionized for A. The possible significance of this fact is unclear to the authors, as is an interpretation of Figure  7.18(a–c). Nevertheless, ionized silanols appear responsible for values of C-7.0. 7.3.4.7  Column Cation-Exchange Capacity C-2.8: Effect of Column Properties Type-A alkylsilica columns exhibit a significant cation-exchange capacity at pH 3 (Figure 7.13), attributable to the presence of acidic silanols that are “activated” by trace metal impurities. Such silanols could be present (in smaller concentrations) in type-B columns as well, resulting in the observed cation-exchange behavior of these columns at low pH. The application of Equation 7.9 (with C-2.8 replacing H) to 167 type-B alkylsilica columns resulted in a correlation of r 2 = 0.423 for C-2.8 as a function of column properties. However, the error (defined as δC-2.8) in the calculated values of C-2.8 is strongly biased for values of C-2.8 < 0.0, as shown in Figure 7.19, where average values of δC-2.8 are plotted for 0.1 increments of C-2.8. As C-2.8 becomes more negative, errors δC-2.8 become progressively larger; this suggests that values of C-2.8 are determined by different stationary-phase entities, depending on whether C-2.8 is greater or less than 0. The latter conclusion is consistent with values of q+ = 0 for C-2.8 > 0 (Figure  7.14a), assuming that values of C-2.8 might be affected by the presence of positive groups within the stationary phase. This suggests that the application of Equation 7.9 (with C-2.8 replacing H) should be restricted to columns with either C-2.8 > 0 or C-2.8 < 0. 7.3.4.8  Values of C-2.8 > 0 The application of Equation 7.9 (C-2.8 replacing H) to 103 columns with C-2.8 > 0 resulted in a correlation of r 2 = 0.63. Additional contributions to C-2.8 from variations in the silica and/or column-packing manufacturing process account for all but © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 333 0.1

Avg. δC-2.8

0.0 –0.1 –0.2 –0.3 –0.4 –0.5 –0.6

y=x –0.4

–0.2 0.0 Avg. C-2.8

0.2

0.4

Figure 7.19  Error in the prediction of values of C-2.8 by means of Equation 7.9 (with C-2.8 replacing H). (Adapted from D. M. Marchand et al. 2011. Journal of Chromatography A 1218:7110.)

11% of the variance in C-2.8 (Appendix 7.2). Figure 7.20 illustrates the dependence of values of C-2.8 > 0 on column properties; as in the case of Figure 7.19 for C-7.0, greater uncertainty is seen in the plots of Figure 7.20. The relative importance of column properties in affecting C-2.8 varies as

n > dpore > CL > end-capping

The contribution of end-capping to values of C-2.8 ≥ 0 (–0.03, Figure 7.20d) is an order of magnitude smaller than for the case of A (–0.32, Figure 7.11d) or C-7.0 (–0.67, Figure  7.18d). The small effect of end-capping on C-2.8 (when C-2.8 > 0) also contrasts with a previous comparison of values of C-2.8 for a Symmetry C18 column (C-2.8 = –0.30), where it was found that end-capping resulted in a decrease in C-2.8 of 0.22 units (versus an average value of 0.03 for columns with C-2.8 > 0). This difference in the effect of end-capping on C-2.8 is likely related to the presence of different ionic sites within the stationary phase for columns with C-2.8 < 0 (e.g., positive sites) or C-2.8 > 0 (negative sites). If ionized silanols are responsible for values of C-2.8 when C-2.8 > 0, why does end-capping have so little effect on stationary-phase ionization? The preparation of RPC columns is usually carried out with an alkyldimethylchlorosilane (primary bonding) and with trimethylchlorosilane (end-capping). In either case, a nonaqueous reaction medium is commonly used with a base B added as catalyst and to neutralize the HCl by-product. Under these reaction conditions, any acidic silanols (those that are ionizable at low pH) might form complexes –SiO –BH+ that could resist reaction with either silane. Reaction of the silane with the silica would then involve mainly silanols that do not ionize at low pH. The latter silanols account for most of the ionized silanols at higher pH, so end-capping is expected to reduce the number of ionized silanols at pH 7, as well as values of C-7.0—with much less effect on the number of ionized silanols at low pH (or values of C-2.8). This speculative proposal could also rationalize the decrease in C-7.0 as ligand concentration CL increases (Figure 7.18c) with the marginal (or opposite) effect on C-2.8 (Figure 7.20c). © 2012 Taylor & Francis Group, LLC

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0.2

0.4

0.1

0.3

C-2.8

C-2.8

0.3

0.0

0

10

20

0.2

30

Ligand Length n 0.1

(a)

C-2.8

015

0.0

0.10 0.05

0

10 20 30 Pore Diameter dpore (nm) (b)

0.00 0

1

2

3

4

5

Ligand Concentration CL (µmoles/m2) (c)

End-capping (–0.03) (no corrected for n, dp, or CL) (d)

Figure 7.20  Dependence of column cation-exchange capacity at pH 2.8 (C-2.8) on column properties (for columns with C-2.8 > 0 only) [51]. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (d) column end-capping. See discussion of Figure 7.6 and the text for other details. (Adapted from D. M. Marchand et al. 2011. Journal of Chromatography A 1218:7110.)

7.3.4.9  Values of C-2.8 < 0 The application of Equation 7.9 (with C-2.8 replacing H) to 58 columns with C-2.8 < 0 gave little correlation of C-2.8 versus column properties (r 2 = 0.14). The dashed line for y = x in Figure 7.19(d) is quite close to the experimental curve for C-2.8 < 0, which supports the conclusion that values of C-2.8 < 0 are largely independent of column properties (n, dpore, CL ). The possible presence of two different ionic groups within the stationary phase—one anionic (silanols) and the other cationic—might explain the poor correlation of values of C-2.8 < 0. In any case, the very different correlations for values of C-2.8 that are 0 argue for different ionic groups in the stationary phase of these two groups of columns. Returning to the behavior of Figure 7.15, how might the different behaviors of these three columns be explained? The Symmetry column shows an increase in k versus pH that contrasts with the slight increase in cation-exchange capacity with pH of Figure 7.13. This can be attributed to the known decrease in q+ with pH [79]. As a result of this decrease in positive charge of the stationary phase, ionic repulsion of the cationic solute will be decreased so that k increases. The faster increase in k with pH for the StableBond column of Figure 7.15 (where q+ = 0) might be a © 2012 Taylor & Francis Group, LLC

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simple consequence of the greater acidity of this column, as indicated by its higher values of C-2.8 (0.14) and C-7.0 (1.04) versus values of C-2.8 (–0.30) and C-7.0 (0.12) for Symmetry C18. The decrease in k for pH > 5 for the Inertsil column may be the result of a decrease in ion-pair retention due to a decrease in the concentration of monocharged citrate at higher pH (the ion-pairing agent) with pH (second pK a = 4.7). 7.3.4.10  Values of C for Other Columns Average values of C-2.8 and C-7.0 have been summarized for different column types (Table 7.2 and reference 46). As expected, type-A alkylsilica columns tend to have higher values of both C-2.8 and C-7.0 than type-B columns because of the use of a more acidic silica. Perfluorophenyl (PFP), fluoroalkyl, and zirconia-base columns have generally larger values of C-2.8 and C-7.0, while embedded-polar-group, phenyl, and cyano columns have values of C-2.8 that are similar to those for type-B alkylsilica columns and values of C-7.0 that are somewhat higher. These differences are likely the result of the particle (type-A or -B silica, zirconia) and/or the individual ligand, but further comment at this time would be excessively speculative.

7.3.5  Hydrogen Bonding α′B Term iv of Equation 7.5 (α′B) appears to represent a hydrogen-bond (H-B) interaction between an acidic (donor) solute and a basic (acceptor) entity X: within the stationary phase (Figure 7.5d). Values of α′ and B refer, respectively, to solute H-B acidity and column H-B basicity. As we will see, the nature of this interaction is considerably less well defined than for the other four interactions (i–iii, v) of Equation 7.5. Furthermore, at least three different basic entities X: appear to exist for different column types, and only in the case of embedded polar group columns can the chemical nature of X: be surmised (see later discussion). For these reasons, the present section is long on details but short on conclusions. Further work is needed to arrive at a description of hydrogen bonding between acidic solutes and basic stationary phases that is compatible with the information summarized in this section. 7.3.5.1  Solute Hydrogen-Bond Acidity α′ The present section will focus on observed relationships between values of α′ and solute molecular properties; however, as we will see, our results are often puzzling. While some attempt will be made to rationalize these discrepancies, a consistent picture of the nature of hydrogen bonding between acidic solutes and basic columns remains to be created. The limited goal of the present section is to summarize our findings as a starting basis for further investigation, with little further attempt at interpretation. For type-B alkylsilica columns, carboxylic acids are the only compound type with consistently large values of α′, as illustrated by the distribution of α′-values in Figure  7.21(a). Values of α′ for aromatic carboxylic acids fall within a range of 0.35 ≤ α′ ≤ 3, accompanied by nine other solutes (0.35 < α′ < 0.65) summarized in Table 7.5(a) and discussed later. Also seen in Figure 7.21(a) is a tendency © 2012 Taylor & Francis Group, LLC

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Lloyd R. Snyder, John W. Dolan, Daniel H. Marchand, and Peter W. Carr 25

1.5

20

1.0 13 Phenols

15

α´

12 Benzoic acids ( )

10 5

R-φ-COOH

0.5

φ-R

0.0 –0.5

–0.5

0.0

0.5

1.0

1.5

3.0

–1.0

0

2

4

6

α´

n´(Number of –CH2-groups)

(a)

(b)

8

1.5 1.0 α´

0.5

α´ 2

φ-R-OH

0.0 –0.5 –1.0

3

R-φ-NH2

1

φ-NHR 0

2

4

6

n´(Number of –CH2-groups) (c)

8

–0.5

Benzoic acid (extrapolated value) –0.3

–0.1

0.1

κ´ (d)

Figure 7.21  Values of solute H-B acidity α′ as a function of molecular structure. (a) Distribution of α′ values for 87 solutes [31]; (b, c) variation of α′ with solute carbon number n′ [31,33]; 4-n-alkylbenzoic acids (R-ϕ-COOH); ω-phenylalkanols (ϕ-R-OH); 4-n-alkylanilines (R-ϕ-NH2); n-alkylbenzenes (ϕ-R); N-n-alkylanilines (ϕ-NHR); (d) variation of α′ for benzoic acids with solute ionization κ′ [31]. See text for details.

for phenols to have somewhat larger values of α′ compared to compounds other than acids. Another solute characteristic that can affect values of α′ is illustrated in Figure 7.21(b): an increase in α′ for solutes with a larger number n′ of –CH2– groups in the molecule. Alkylbenzenes (•) have no H-B acidity in solution (αH2 = 0), and their values of α′ increase only slightly with n′; 4-n-alkylbenzoic acids (o) show a much greater increase in α′ with n′. Figure  7.21(c) shows similar plots for three other homologous series of H-B bases: ω-phenyl-1-alkanols (o), 4-n-alkylanilines (◾), and N-n-alkylanilines (•). Compared to the nonpolar alkylbenzenes, there is a five- to sevenfold stronger dependence of α′ on n′ for solutes that are H-B donors in solution: alcohols (αH2 = 0.3), carboxylic acids (αH2 = 0.6), and anilines (αH2 = 0.3) [71]. Note that extrapolated values for non-alkyl-substituted alcohols and anilines (i.e., for n′ = 0) are negative; this implies that these functional groups are “antidonors” because α′ ≈ 0.1 for most nondonor solutes. All of this is puzzling, especially because the number of –CH 2– groups in alkyl substituents has almost no effect (for n′ > 2) on solute H-B acidity (αH2 ) in solution. Steric hindrance, as in the case of H-B acceptor solutes © 2012 Taylor & Francis Group, LLC

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Table 7.5 Solutes Other Than Carboxylic Acids with Extreme Values of α′ α′

Solute

Comment

(a) Solutes with large values of α′ (α′ > 0.3)   1. Amitriptyline   2. 5-Phenyl pentanol   3. Nortriptyline   4. Fisetin hydrate   5. 4-n-Hexylaniline   6. 4-n-Heptylaniline   7. Oxazepam   8. 2,3 Dihydroxynaphthalene   9. Coumarin

0.35 0.37 0.38 0.41 0.42 0.58 0.58 0.61 0.65

Strong base Large n′ (Figure 7.21c) Strong base –(OH)C=C(OH)– Large n′ (Figure 7.21c) Large n′ (Figure 7.21c) –C(=O)–C(OH)– –(OH)C=C(OH)– None

(b) Solutes with large negative values of α′ (α′ < –0.3) 10. N-ethylaniline 11. Prolintane 12. 5,5 Diphenylhydantoin 13. N-butylaniline 14. Propranolol

–0.58 –0.53 –0.45 –0.35 –0.33

Large n′ (Figure 7.21c) Strong base None Large n′ (Figure 7.21c) Strong base

(Table 7.4, Figure 7.10), cannot be an explanation because values of α′ decrease for larger values of n′. There is a strong correlation of values of α′ and κ′ for benzoic acids not substituted by alkyl groups (Figure 7.21d):

α′ = 0.63 – 5.6 κ′   (r 2 = 0.96, n = 9, SE = 0.17)

(7.18)

For 4-n-alkylbenzoic acids in Figure 7.21(b), the extrapolated values for n′ = 0 is α′ = 0.4 and κ′ = 0.02; this data point (for benzoic acid) falls close to the correlation line in Figure 7.21(d). More negative values of κ′ for acids correlate with increasing ionization (Section 7.3.4), so Equation 7.18 suggests that values of α′ are a result of (a) the repulsion of ionized acids from a negatively charged stationary phase, or (b) anion exchange with a positively charged column. The latter seems somewhat unlikely because there is no correlation of values of B and q+ (r 2 = 0.002, n = 12; values of q+ from reference 47)—as would be required for either anion exchange or ionic repulsion. An alternative interpretation of Equation 7.18 is that more negative values of κ′ reflect an increase in Brønsted acidity, which in turn should parallel solute H-B acidity. The relationships summarized previously are consistent with an increase in α′ for more acidic benzoic acids—which supports hydrogen bonding by an acidic solute as

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the basis of the α′B term. However, values of α′ for different compound types do not correlate well with their H-B acidity in solution (αH2). Phenols and carboxylic acids have the same solution acidity (αH2 = 0.6), but α′-values for phenols are an order of magnitude smaller than for benzoic acids. Similarly, alcohols and anilines with αH2 = 0.3 should have α′-values half as large as carboxylic acids; however, Figure 7.21(b) suggests negative values of α′ for both anilines and alcohols after correction for alkyl substitution (i.e., for n′ = 0). This failed correlation of values of αH2 and α′ is somewhat reminiscent of a similar lack of correlation for values of β2 and β′ (Table 7.4, Figure 7.10a) but as noted above cannot be an explanation for values of α′. If the α′B term indeed measures hydrogen bonding between solutes and type-B alkylsilica columns, then carboxylic acids are much more effective donors than expected when compared with phenols, anilines, and alcohols. The marked dependence of values of α′ on alkyl substitution n′ remains puzzling. Returning to solutes other than carboxylic acids with values of α′ > 0.3 (Table 7.5a), three of these solutes (solutes 2, 5, and 6) are proton donors with long alkyl chains (as in Figure 7.21b), and three other solutes are more acidic phenols (solutes 4 and 8) or alcohols (solute 7). Their higher values of α′ are therefore unsurprising. The remaining three nonacidic compounds (1, 3, and 9) do not fit into any obvious category. It should also be noted that there are five solutes with very negative values of α′ (Table  7.5b). Because most neutral solutes have values of α′ ≈ 0, negative values imply “antidonor” behavior but this makes little physical sense. Two of these solutes (10 and 13) are N-alkylanilines with short alkyl groups; their negative values are consistent with the behavior of the 4-n-alkylanilines of Figure 7.21(c), whose α′ values extrapolate to negative values for aniline. Two of the solutes of Table 7.5(b) are strong bases (11 and 14), with very different values of α′ versus values for the two other strong bases of Table 7.5(a) (1 and 3). Because there is only one other strong base whose value of α′ has been measured (diphenhydramine, α′ = 0.16), it appears that strong bases may generate anomalous values of α′ (possibly connected to the dependence of α′ on κ′ for acids [Equation 7.18]). Compound 12 represents another example (as for solutes 1, 3, and 9 of Table 7.5a) of unexpected behavior, all of which might simply reflect experimental error in values of α′. 7.3.5.2  Column Hydrogen-Bond Basicity B versus Hydrophobicity H Early in the present program, a moderate correlation was noted for values of B versus H for type-B alkylsilica columns (r 2 = 0.62 [34]). A similar correlation exists for the present 167 columns:

B = 0.115 – 0.124 H   (r 2 = 0.57, SE = 0.014)

(7.19)

as illustrated in Figure 7.22(a) (see later discussion for ±2 SE limits in Figure 7.22, shown as “---”). Some correlation among values of H, S*, etc. is expected, as each of these column parameters is affected by the same column properties (n, dpore, CL , and end-capping). Except for B and H, however, the average correlation of column selectivity parameters (H, S*, etc.) for the same 167 columns is relatively modest (r 2 = 0.14 ± 0.16) compared to r 2 = 0.57 for Equation 7.19. © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 339 0.08 0.06

B

0.08

Type-B alkylsilica

0.04

0.04

0.02

0.02

0.00

0.00

–0.02

–0.02

–0.04 –0.06 0.4

B = 0.115 – 0.124 H r 2 = 0.57, SD = 0.014 0.6

Type-B alkylsilica

0.06

–0.04

0.8

1.0

1.2

(a)

–0.06 0.4

0.6

0.8

1.0

0.4

0.10

Cyano

1.2

(b)

H

EPG

0.3

0.05

0.2

B

0.1

0.00

0.0 0.3

0.5

0.4 (c)

0.25

B

0.2

0.6

0.6

H

0.8

0.08

Type-B alkylsilica

1.0

1.2

(d)

0.15

0.04

0.05

0.00

AQ

–0.04

–0.05 0.4

0.4

0.6

0.8 (e)

1.0

1.2

H

0.5

0.7

0.9

1.1

(f)

Figure 7.22  Column H-B basicity B versus hydrophobicity H for different column types. (a) Type-B alkylsilica columns; (b) average values for data of (a) for subsets of similar H; (c) cyano columns; (d) embedded polar group columns; (e) type-A alkylsilica columns; (f) polar end-capped (“aqua”) columns [52]. Added lines (---) represent ±2 SE for data of (a). See text for details.

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The apparent correlation of Equation 7.19 and Figure 7.22(a) is worth pursuing for two reasons. First, the approximate dependence of column H-B basicity B on hydrophobicity H may provide some insight into the nature of column basicity for type-B alkylsilica columns. Second, it will prove informative to compare the dependence of B on H for other kinds of columns with that for type-B alkylsilica columns. Before exploring these possibilities, however, a better description of the data of Figure 7.22(a) is needed than is provided by Equation 7.19. A quadratic dependence of B on H provides a somewhat better fit than the linear dependence of Equation 7.19, but data for either small or large H still deviate noticeably. A more accurate representation of the data can be inferred as follows. Subsets of the data for n columns of similar H can be averaged, and a standard error calculated for each subset. The accuracy (as opposed to precision) of an average value can be estimated as SE/(n – 1)1/2. Resulting values of B versus H are plotted in Figure 7.22(b) with the latter accuracy estimates (shown as |). Figure 7.22(b) suggests that a bilinear equation best represents the dependence of B on H:

(for H ≤ 0.97)   B = 0.08 – 0.08 H   SE = 0.013 (n = 149)

(7.20)



(for H ≥ 0.97)   B = 0.35 – 0.36 H   SE = 0.011 (n = 105)

(7.21)

No fundamental significance of combined Equations 7.20 and 7.21 is proposed at this point; we only assume that these relationships provide a more reliable empirical representation of the data. On the basis of Equations 7.20 and 7.21, ±2 SE limits (---) have been superimposed on the data of Figure 7.22(a). We will next examine the dependence of B versus H for other column types, using the error limits of Figure 7.22(a) for comparison with type-B alkylsilica columns. 7.3.5.3  B versus H for Other Column Types Phenyl columns show a similar correlation of values of B versus H, with only 4 of 37 columns falling outside the error limits of Figure 7.22(a) (data not shown). Cyano columns (Figure 7.22c) have values of B that are generally lower than those for typeB alkylsilica columns. However, the error limits shown in Figure 7.22(c) (---) end at H = 0.4 (Figure 7.22a); it is possible that the dependence of B on H changes for values of H < 0.5 as suggested by the best-fit line (…) of Figure 7.22(c) (with corresponding error limits). More interesting are plots of B versus H for EPG columns (Figure  7.22d) and type-A alkylsilica columns (Figure 7.22e). For each of the latter two column types, values of B are often much larger than expected, while other values cluster within the error limits for type-B alkylsilica columns. This suggests that values of B for these latter columns are determined by the same process or H-B basic entity as for type-B alkylsilica columns, plus—for those columns enclosed within the dashed ellipses of Figure 7.22(d, e)—some additional contribution to B. A final comparison of B versus H is shown in Figure  7.22(f) for 10 columns designated by such terms as “aqua,” “AQ,” “aqueous,” and “hydrosphere.” These columns have been designed to resist stationary-phase de-wetting and, in most cases, they are believed to incorporate polar group end-capping [72]. As can be seen in © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 341

Figure 7.22(f), values of B versus H for these columns appear little different from those for columns without such end-capping. This suggests that whatever the source of H-B basicity in type-B alkylsilica columns, it is not affected by polar end-capping. 7.3.5.4  B as a Function of Column Properties (Type-B Alkylsilica Columns) Values of B can also be correlated with column properties (Equation 7.9 with B replacing H [50]). The latter relationship accounts for about 62% of the variance of values of B, while all but ~6% of the remaining variance appears due to differences in the silica and other changes in the manufacturing process (Appendix 7.2). Plots of B versus column properties are shown in Figure 7.23, just as for H in Figure 7.6 (dashed curves again represent an estimate of the uncertainty in these plots). The dependence of B on each column property is the opposite of that observed for H— as might be anticipated from the inverse dependence of B and H (Equation 7.19; Figure 7.22a). For example, H increases with ligand length n while B decreases, H decreases with pore diameter dpore while B increases, etc. 7.3.5.5  The Origin of Hydrogen-Bond Basicity for Different Columns Previously [33,39], it was suggested that the H-B basicity of type-B alkylsilica columns can be attributed to water held within the stationary phase. The amount of sorbed water should increase with stationary-phase polarity or inversely with column hydrophobicity

0.04 0.02

0.02 B

0.00

B

–0.02

–0.02 –0.04

0.03 0.02 B 0.01 0.00 –0.01

0.00

0

10

20

30

–0.04

0

10

20

Ligand Length n

Pore Diameter dpore (nm)

(a)

(b)

30

End-capping (–0.01) (no correction for n, dp, or CL) 0

1

2

3

4

5

(d)

Ligand Concentration CL (µmoles/m2) (c)

Figure 7.23  Dependence of column H-B basicity B on column properties [52]. (a) Ligand length n; (b) pore diameter dpore; (c) ligand concentration CL; (d) column end-capping. See discussion of Figure 7.6 for other details. © 2012 Taylor & Francis Group, LLC

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H, as very approximately observed. It was also suggested that carboxylic acids might bind water more strongly by chelation, which might explain the much larger values of α′ for carboxylic acids compared to other donor solutes such as phenols, anilines, and alcohols. It is believed that stationary-phase water is held by silanols at the ligand– silica interface [82], so values of B should increase with an increase in the number of silanols, if B depends on the amount of water in the stationary phase. Based on the following evidence an increase in B with silanol content appears questionable. End-capping removes silanols and should therefore reduce water content and values of B. However, the effect of end-capping on values of B is relatively modest in comparison with the dependence of B on other column properties (Figure 7.23). If silanols were responsible for values of A (as appears likely) as well as B, then the dependence of A and B on column properties should be similar. However a comparison of Figures 7.11 and 7.23 shows no such similarity; rather, the dependence of B on n, d pore, and CL is opposite to that of A, while end-capping has a large effect on A but not B. The generally greater values of B for EPG columns have been attributed to basic polar groups (carbamate, urea, amide) that form part of the ligands of these columns, while larger values of B for type-A alkylsilica columns might be related to metal contamination. So far we have assumed that values of the solute parameters η′, σ′, etc. are constant for a given solute and different columns, and we have used these values for measuring the parameters H, S*, etc. for different columns. However this approach results in larger errors for the application of Equation 7.5 to columns other than type-B alkylsilica (Section 7.3.7). Much better fits by Equation 7.5 of values of log k for these columns can be obtained by repetitive regressions with alternating use of either solute or column parameters from the preceding regression (as in the original derivation of Equation 7.5 for type-B alkylsilica columns). Resulting (column-type-dependent) values of α′ for donor solutes are shown for three column types in Table 7.6; these values of α′ more accurately represent the interactions of a solute with a given column type. It is seen in Table 7.6 that phenols are much more effective donors (larger values of α′) for EPG columns than for either type-A or -B alkylsilica columns. That is, relative to type-A or -B alkylsilica columns, phenols are retained more strongly on EPG columns of similar basicity (similar values of B). These values of α′ for phenols versus carboxylic acids also more nearly mirror their corresponding value of H-B acidity (αH2 ) in solution. Smaller values of α′ for phenols with type-A versus EPG columns suggest that the source of excess column basicity in EPG and type-A columns is not the same. Thus, three different sources of column basicity are suggested: (a) that observed for type-B alkylsilica columns (but assumed present in all columns), (b) the “excess” basicity observed for EPG columns, and (c) the “excess” basicity seen for type-A alkylsilica columns. Apart from the apparent presence (in various columns) of three different basic entities (as noted earlier), certain confusing facts remain for type-B alkylsilica columns (and other columns whose values of B correlate with values of H): • Values of α′ for different functional groups (–COOH, –OH, –NH2) bear little resemblance to their H-B basicity in solution. © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 343

Table 7.6 Values of α′ for Phenols and Benzoic Acids as a Function of Column Type α′ Solute 4-Nitrophenol p-Chlorophenola 4-n-Butylbenzoic acid Mefenamic acid

Type Ba

Type Aa

EPGb

0.22 0.15 1.02 0.92

0.10 — 0.84 1.12

0.83 0.67 1.09 1.30

Note: Values from repeated regression of Equation 7.5 for different column types. a Alkylsilica columns (J. J. Gilroy et al. 2004. Journal of Chromatography A 1026:77). b Embedded polar group columns (N. S. Wilson et al. 2004. Journal of Chromatography A 1026:91).

• Values of α′ are significantly larger for higher homologs of acids, anilines, and alcohols (Figure 7.21b, c). • End-capping with either the usual trimethylsilyl (TMS) or polar groups has little (if any) effect on column basicity. • There is so far no basic entity within the stationary phase of type-B alkylsilica columns that can be reconciled with the dependence of α′ on column properties (especially the effects of end-capping, as noted above). Further studies are required before even a partial picture can emerge of the origin of column H-B basicity in columns other than those with embedded polar groups. 7.3.5.6  Values of B for Other Columns With the exception of embedded polar group columns, average values of B for different column types generally fall within a narrow range (±0.02), as seen in Table 7.2.

7.3.6  Other Solute–Column Interactions In the case of phenyl [41,42,73,83] and cyano [42,83] columns, it has been shown that π–π interaction as in Figure 7.5(g, h) is possible for aromatic solutes—especially those substituted by –NO2 groups. Similarly, dipole–dipole interactions as in Figure 7.5(f) can occur with cyano columns and strongly dipolar alkyl groups (e.g., –(CH2)n–C ≡ N or –(CH2)n–NO2). The effects of each of these two interactions on retention are reduced with acetonitrile as B-solvent, compared to the use of methanol [42]. In each case, acetonitrile can better compete with the solute for a place in the stationary phase or tie up the solute in the mobile phase by taking part in either π–π or dipole–dipole interactions. Even with methanol as B-solvent, π–π interactions are significant for only © 2012 Taylor & Francis Group, LLC

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a limited number of solutes. Similarly, dipole–dipole interactions are generally less important than other interactions in affecting solute retention. For this reason, these two interactions can often be ignored for phenyl or cyano columns, and they are insignificant for other column types (but see the discussion of Euerby et al. [73]). In Section 7.3.2 we noted that steric interaction (term ii of Equation 7.5) is similar to but different from shape selectivity. Consequently, shape selectivity is a third interaction not incorporated into Equation 7.5. For various reasons, polymeric columns (for which shape selectivity is most pronounced) are less used today for RPC separation. Additionally, shape selectivity has been shown to be important for only a limited range in solute structure. For these reasons, the failure of Equation 7.5 to take shape selectivity into account is of limited practical significance. Finally, it is possible for some solutes to chelate with metals that are incorporated (either intentionally or, more often, accidentally) into the stationary phase. Chelation is rarely observed (usually only for type-A columns), and its importance is generally negligible for columns in common use today. In principle, it would be possible to incorporate additional terms into Equation 7.5 for each of the latter four interactions, but the required experimental effort would be excessive when compared to its expected advantage.

7.3.7  Error in the Model The accuracy of Equation 7.5 for type-B alkylsilica columns (avg. SE = 0.004) is an order of magnitude better than that of Equation 7.1, which was previously the most reliable general relationship for predictions of k as a function of the column and other conditions. As summarized in the second column of Table 7.7(a), however, Equation 7.5 can be much less reliable for columns other than type-B alkylsilica, with average SE values that are 7 to 40 times larger. Various explanations can be offered for these larger errors, including the possible presence of solute–column interactions other than those represented by terms i–v of Equation 7.5. For example, we have noted that π–π interactions are possible for phenyl and cyano columns, as are dipole–dipole interactions for cyano columns (Section 7.3.6). It has also been suggested [35] that error can arise when Equation 7.5 is extrapolated beyond the range of values of H, S*, etc. found for type-B alkylsilica columns. The cause of these larger errors in Equation 7.5 for other columns is an important question that we will now examine more closely. For a limited number of alkylsilica, EPG, and zirconia-base columns, it was reported [35] that error in Equation 7.5 can be described by

SE = a |H-Hb | + b | S*-S*b | + c | A-Ab | + d | B-Bb | + e | C-Cb |

(7.22)

Here, the observed standard error for the application of Equation 7.5 to a given column is related to the selectivity parameters of that column (H, S*, etc.) and to average values of these parameters for all type-B alkylsilica columns (Hb, S*b, etc.; see values in Table 7.7b, footnote f). We have since reapplied Equation 7.22 © 2012 Taylor & Francis Group, LLC

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The Hydrophobic-Subtraction Model of Reversed-Phase Column Selectivity 345

Table 7.7 Error in the Application of Equation 7.5

Column Type

Avg SDa

Total Number of Columnsb

Number of Excluded Columnsc

Avg. Bd

0 0 8 2 5 3 3

0.002 0.021 0.015 0.00 0.002 0.146 0.047

(a) For Various Column Types Type-B alkylsilica Phenyl Type-A alkylsilica Cyano Fluoroe EPG Zirconia

0.004 0.028 0.032 0.041 0.059 0.080 0.157

88 22 58 20 8 38 3

(b) Dependence of Error on Column Parameters (Equation 7.22f) Regression results (Equation 7.22): r2 0.876 SE 0.010 0.012 (Ha) 0.046 (S*b) (Ac) 0.033 0.335 (Bd) (C-2.8e) 0.002 a b c

d e f

Average SD for representative columns. Number of columns of this type tested by Equation 7.22. Number of tested columns deleted from Equation 7.22 (predicted values of SE deviated from actual values by >3 SE). Average value of B for tested columns. PFP and fluoroalkyl columns combined. With Hb = 0.92; S*b = –0.01; Ab = –0.15; Bb = 0.00; Cb (C-2.8 ) = 0.04.

to a much larger and more diverse set of columns as noted in the third column of Table 7.7(a). The final regression (with r 2 = 0.876) is summarized in Table 7.7(b), after deletion of 21 columns (9% of the total) whose values of SE predicted by Equation 7.22 were in error by three or more times the value of SE = 0.010 for the regression of Equation 7.22. Consider first those columns that are poorly described by Equation 7.22, thereby resulting in the deletion of a large fraction of columns of that type from the regression (see third and fourth columns of Table 7.7a). All three zirconia-base columns are poorly correlated by Equation 7.22, with average errors in values from Equation 7.22 of 12 SD. This can be attributed to the very different nature of these columns, which consists of physically coating a zirconia surface with the stationary phase. As a consequence, the use of Equation 7.5 and the H-S model may be inappropriate for © 2012 Taylor & Francis Group, LLC

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zirconia-base columns. Similarly, five out of eight fluoro-substituted columns fail to correlate well with Equation 7.22; these columns exhibit unusually low dispersion interactions with the solute [41], an effect that is not recognized by Equation 7.5. Remaining columns that were excluded from the application of Equation 7.22 gave predicted values of SE that were positive in eight out of ten cases. We have no comment on these latter exceptions to Equation 7.22. Only 5% of cyano plus phenyl columns were excluded because of excessive error in Equation 7.22, whereas these columns are capable of interactions (π–π, dipole– dipole) that are not represented in Equation 7.5. That is, the omission of these interactions from Equation 7.5 seems to play little part in the relative inaccuracy of Equation 7.5 for phenyl and cyano columns when applied to the 16 test solutes used to measure values of H, S*, etc. (This may reflect the fact that these test solutes do not include compounds likely to exhibit strong π–π or dipole–dipole interactions with the column [42].) Referring to the regression results of Table  7.7(b) for columns that were not excluded, by far the largest contribution to error is associated with values of B (for which the error coefficient d = 0.335). From our discussion of B for different column types in Section 7.3.5, it appears that different entities X: may be responsible for basicity in type-A alkylsilica, type-B alkylsilica, and embedded polar group columns. Because only a single measure of column H-B basicity is recognized by Equation 7.5, this multiplicity of basic entities in different columns is likely the main reason for large errors in Equation 7.5 that are associated with the column parameter B. In conclusion, error in Equation 7.5 when applied to different column types seems a natural consequence of two considerations: (a) an increase in error for columns whose values of H, S*, etc. (especially B) differ from average values for type-B alkylsilica columns (because all column parameters are derived from solute parameters for type-B alkylsilica), and (b) the presence of different proton acceptors in the stationary phase. There seems no obvious possibility for reducing error in Equation 7.5, other than by restricting its application to columns with smaller values of B.

7.4  Applications of Column-Selectivity Measurements Previous sections have described the H-S model and examined the relationship of the solute and column parameters of Equation 7.5 to solute molecular structure and column properties, respectively. On the basis of these observations, it appears that these column parameters describe specific, fundamental characteristics of the column: hydrophobicity H, steric interaction S*, etc. If this is the case, then values of H, S*, etc. should be related to various phenomena of interest to users of RPC. At present, some promising examples of this kind have been demonstrated, while other logical possibilities remain to be explored. The present section will attempt to address both real and possible applications of the H-S model, as an incentive for continued exploration of this area. The reader is encouraged to consider still other possible applications that might depend on fundamental properties of the column. © 2012 Taylor & Francis Group, LLC

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7.4.1  Comparing Columns in Terms of Selectivity Selectivity is by definition a relative concept. Thus, there is no such thing as a generally more selective column. There are only columns that differ in selectivity, as in the examples of Figure 7.1. This being the case, we need some means for measuring differences in column selectivity. As an example, separation selectivity is often compared by plots of log k for one set of conditions versus another, as in Figure 7.2(a) for two different columns (with other separation conditions unchanged). The similarity of the two separations can then be characterized by either the coefficient of determination r 2 or the standard error (SE) of the fit, with the use of values of r 2 more common. When comparing column selectivity in this way, however, values of SE can be directly related to differences in the separation factor α and the resolution of adjacent peaks in the separation [34]; SE may therefore be a better choice for quantitative comparisons of selectivity. The selectivity of two columns, 1 and 2, can also be defined by the differences in their values of H, S*, etc. A single combined measure of the difference in selectivity of two columns is more convenient in practice; for example, the distance Fs′ between the positions of the two columns in five-dimensional space (defined by values of H, S*, etc.) is given as

Fs′ = [(H2 – H1)2 + (S*2 – S*1)2 + (A2 – A1)2 + (B2 – B1)2 + (C2 – C1)2]1/2

(7.23)

Equation 7.23 assumes that each of these five parameters (H, S*, etc.) has an equivalent effect on column selectivity, which is generally not true. This is illustrated in Table 7.8 for a sample composed of 87 compounds of widely different molecular structures. It is seen that a change in H by 0.01 unit (second column of Table 7.8)

Table 7.8 Derivation of Weighting Factors for Equation 7.23 Column Parameter

Change in log α for Change in Parameter by 0.01 unitsa

Allowed Change in Parameterb (Δ)

Weighting Factor in Equation 7.23(a)c

0.0005 0.0041 0.0012 0.0061 0.0033

0.080 0.010 0.033 0.007 0.012

12.5 100 30 143 83

H S* A B C

Note: Based on data for 67 solutes and 10 different columns (J. Gilroy et al. 2003. Journal of Chromatography A 1000:757). a Average absolute value of the change in log α when a parameter is changed by 0.01 unit (for a sample containing 67 solutes). b Allowed change in parameter for average 1% change in α (equal “Δ”). c Equal to 1/Δ.

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results in an average (absolute) change in log α of 0.0005, whereas the same 0.01 unit change in B results in a 12-fold larger change in log α (0.0061), with intermediate changes for other parameters. If a 1% change in α is allowed for a change of each parameter, resulting allowed changes Δ in each parameter are shown in the third column of Table 7.8. Values of Δ can then be used as weighting factors (1/Δ) to correct Equation 7.23:

Fs = {[12.5 (H2 – H1)]2 + [100 (S*2 – S*1)]2 + [30 (A2 – A1)]2 + [143 (B2 – B1)]2 + [83(C2 – C1)]2}1/2

(7.23a)

Equation 7.23(a) was tested for a subset of 67 solutes and 10 different type-B alkylsilica columns as follows. Values of log k for all solutes and column pairs were successively plotted versus each other to generate 50 comparisons (i.e., column 1 versus column 2, 1 versus 3, 2 versus 3, etc.) and associated values of SE for each pair of columns. The latter values of SE quantitatively characterize differences in column selectivity, so there should be (and is) a correlation of values of SE and Fs from Equation 7.23(a):

SE = 0.006 + 0.0027 Fs   (r 2 = 0.945, SE = 0.007)

(7.24)

For this particular 67-compound sample, values of Fs therefore provide a good prediction of comparative column selectivity (expressed as values of SE). An example of the use of Equation 7.23(a) is provided by the three columns of Figure 7.1. The value of Fs for the Ace C18 column versus the XTerra MS C18 column is 2.5 (a small value), and the two separations are quite similar. The value of Fs for the Spherisorb ODSB column versus the XTerra MS C18 column is much larger (Fs = 88), and the two separations are very different. For other samples or mixtures of solutes, Equation 7.23(a) can be less accurate [38] because the weighting factors in Equation 7.23(a) (12.5, 100, etc.) depend on the sample (i.e., values of the solute parameters η′, σ′, etc. for the different sample components). Nevertheless, Equation 7.23(a) is preferable to assuming equal weighting factors for all five parameters as in Equation 7.23. Some improvement in Equation 7.23(a) is possible when information on the nature of the sample components is available. Thus, if no ionized compounds are present in the sample, the last term of Equation 7.23(a) [83(C2 – C1)] can be dropped. Similarly, for columns other than those with embedded polar groups, values of α′ are ~0 for compounds other than acids. The next to last term of Equation 7.23(a) [143 (B2 – B1)] can therefore be set to zero when carboxylic acids are absent from the sample. Software that allows the use of Equation 7.23(a) as previously described for selecting columns of either similar or different selectivity can be accessed at the United States Pharmacopeia website: http://www.USP.org/USPNF/columns.html or from the Molnar Institut, Berlin. (Column Match). Either of these two softwares currently allows comparisons among >500 different reversed-phase columns for which values of H, S*, etc. have been measured, and ~50 new columns are added each year.

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Similar software is available for other procedures that characterize column selectivity (Section 7.5). The use of Equation 7.23(a) for selecting columns of similar selectivity assumes that column selectivity does not change appreciably from one manufacturing batch to another. For two batches each of 11 different columns (unpublished data), the following average repeatability (1 SE) was found for each column parameter (H, 0.007; S*, 0.005; A, 0.020; B, 0.001; C-2.8, 0.022; C-7.0, 0.038). The latter batch-to-batch repeatability values are only slightly greater than the experimental imprecision of measured values of H, S*, etc. (Table 7.2). Other studies suggest that selectivity does not vary much among nominally equivalent virgin columns from different production batches [26–30], in agreement with the latter data.

7.4.2  Choosing Columns of Similar Selectivity HPLC columns can degrade during use, requiring their eventual replacement. When a new column is needed for a routine assay, the same or similar separation is required. In most cases, a nominally equivalent column of the same part number (e.g., Waters Symmetry C18) can be expected to provide a sufficiently similar selectivity and separation [25–30]. This may not always be the case, however, for various reasons. For example, although the minor variability of column selectivity from batch to batch is normally not enough to affect the separation of most samples adversely, this might not be true for a particularly demanding separation. Furthermore, a column bought today may not be available at some time in the future. In either case, a column of different part number but similar selectivity must then be found; this often is referred to as an “equivalent” column in method documentation. Equation 7.23(a) provides a convenient basis for identifying other columns that might be substituted for the original column and therefore provide an equivalent separation. Regulatory agencies may require the revalidation of a method when a similar column is substituted in a routine procedure (see Section 12.8 in reference 72). It can be estimated [34] that if Fs ≤ 3 for two columns 1 and 2, differences in α should be ≤3%, and the two columns are likely to provide equivalent selectivity and separation for various samples and separation conditions. Larger values of Fs may be acceptable, especially for “easy” separations where the critical resolution Rs >> 2. Figure 7.24 illustrates the use of Fs -values for selecting equivalent columns for two demanding separations that feature the gradient separation of two different pharmaceutical samples. In Figure 7.24(a–d), separations with the original (a) and three replacement columns (b–d) are shown with their values of Fs (compared to the Luna column in Figure 7.24a). Essentially equivalent results for all peaks of interest (marked by *) are obtained in Figure 7.24(a–c), where Fs ≤ 2 for these three columns. For a column with Fs = 10 (Figure 7.24d), however, the last two peaks in the chromatogram have merged together (i.e., with unacceptable resolution). A comparable example is shown in Figure 7.24(e, f), where a value of Fs = 1 again yields an almost identical separation. See reference 38 for several other examples where similar separation was found for replacement columns with small values of Fs.

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Figure 7.24  Selection of “equivalent” columns based on values of Fs. (a–d) Separations of a proprietary sample on four different columns; values of Fs calculated versus “original columns” of (a); (e, f) similar separations for a second proprietary sample [38,94].

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7.4.3  Choosing Columns of Different Selectivity Just as two columns with small values of Fs (Equation 7.23a) will have similar selectivity, columns with large values of Fs will differ in selectivity, as was demonstrated in a recent study for a sample of 19 pharmaceutical drugs and 14 different RPC columns [84]. It was found that an experimental column (sulfonated hyper-cross-linked C8 phase [85]) possessed a selectivity that was significantly different from the other 13 columns studied (as measured by SE values for log k–log k plots). Columns that differ markedly in selectivity are often referred to as “orthogonal,” which implies a correlation of r2 ≈ 0.00 (or a large SE) for separations carried out by two such columns. While r2 ≈ 0.00 is rarely observed for two RPC columns and samples of diverse composition, we will arbitrarily refer to two columns as “orthogonal” when their selectivities are quite different. A large change in column selectivity—such as by the use of orthogonal columns—can be useful for different reasons: • To improve resolution during method development • To develop an orthogonal method to complement a primary separation, so as to avoid “hidden” peaks [43] • For thermally tuned tandem-column separations [86] • For two-dimensional (2-D; LC × LC) separations [87] A variety of column-comparison procedures have been used for the selection of orthogonal columns [88]. An improvement of resolution during method development is usually best achieved by a change in separation selectivity [72]. Of the various means for changing selectivity, a change in column is one of the most effective [43]. “Hidden” peaks are compounds that are overlapped by another peak in the chromatogram and are not known to be present in the sample. Hidden peaks are often much smaller than the overlapping peak and are usually either trace components or unexpected impurities. Once a “primary” separation has been developed for a sample, it is recommended to develop a complementary orthogonal separation [43]. Any peaks hidden in the primary separation are likely to be resolved in the orthogonal separation. Tandem-column and two-dimensional separations use two connected columns, where fractions from the first column are diverted to one or more secondary columns for further separation. In each case, the primary and secondary columns should be “orthogonal.” The use of two RPC columns for two-dimensional HPLC is less common because greater “orthogonality” can usually be obtained by the combined use of RPC with some other separation mode (e.g., ion exchange). However, the use of two orthogonal RPC columns may be preferred in some situations. A good example of the use of Equation 7.23(a) to select orthogonal columns is provided by a recent example of three-dimensional separation, where it was possible to select three columns, each of which had Fs > 140 when compared to the other two columns [89]. Because values of Fs are largely determined by differences in C for the two columns ([46]; see also reference 5) and because the separation of many sample components is unaffected by values of C, it is recommended [48] that “orthogonal” columns be

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chosen on the basis of maximum values of both Fs and Fs(–C) [48], where Fs(–C) is given by Equation 7.23(a) with the C-term—[83(C2 – C1)]2—omitted:

Fs(–C) = {[12.5 (H2 – H1)]2 + [100 (S*2 – S*1)]2 + [30 (A2 – A1)]2 + [143 (B2 – B1)]2}1/2



(7.25)

Two RPC columns with Fs > 100 and Fs(–C) > 50 can be regarded as “orthogonal” (i.e., as different in selectivity as possible) for an average sample.

7.4.4  Anticipating Peak Tailing Tailing peaks can occur for many reasons [72]. When more than ~1 μg of a solute is injected into a column of standard diameter (4–5 mm), ionized compounds can tail in RPC as a result of ionic repulsion among solute molecules within the stationary phase [90]. Prior to the introduction of type-B columns in the 1980s, protonated bases often exhibited peak tailing, even for very small samples. One study, cited in Appendix C of reference 34, showed moderate peak tailing occurring at pH 6 for protonated bases and columns with values of C (C-6.0) between 0.3 and 0.6, with severe tailing for C-6.0 > 0.6. Another study of peak tailing for protonated bases at pH 2.8 (30 mM phosphate buffer) reported little tailing when C-2.8 ≤ 0.3 [46] (Figure 7.25a). Comparable data for berberine as solute and pH 7.0 are plotted in Figure  7.25(c, d) versus either C-2.8 or C-7.0, respectively. It appears that a somewhat better correlation is obtained for values of C-2.8 than for C-7.0. Peak tailing of bases generally increases for lower buffer concentrations and larger values of C-2.8 [51]. Other data show that newer (type B) columns have C-2.8 ≤ 0.3 (Section 7.4.8), while older (type A) columns have C-2.8 > 0.3; this suggests that peak tailing for protonated bases may be related to the metal contamination of type-A columns. Any generalizations concerning peak tailing for basic solutes as a function of the column should be qualified, however, because of a considerable variation in tailing among different basic solutes and for different conditions [91]. The tailing of carboxylic acids is less common, but has been noted for both types-A and -B alkylsilica columns [46]. Peak tailing tends to correlate with “excess” column basicity B", defined as

B" = B – (predicted value of B from Equation 7.20)

(7.26)

As seen in Figure 7.25(b), no tailing of acids has been observed for type-B columns with values of B" ≤ 0. On average, the tailing of acids tends to increase with values of C-2.8 for type-A columns [46]. Peak tailing for small sample weights likely arises from strong, slowly reversible binding of the solute to “strong” sites within the stationary phase: acidic (cationic) sites for basic compounds and basic (anionic) sites for acids. Values of C for RPC columns are an indirect measure of the acidity of the unbonded silica particle and can © 2012 Taylor & Francis Group, LLC

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12

Protonated Bases (pH-2.8)

10 8 As

10 C-2.8 = 0.05

8

As

6

4

2

2 0.0

1.0 C-2.8

0 –0.10

2.0

B´´ = 0.00

6

4 0 –1.0

Carboxylic (pH-2.8)

12

–0.05

16

16

12

As 12

8

8

4

4 0.0

0.5 C-2.8 (c)

0.10

0.15

Berberine (pH-7.0)

Berberine (pH-7.0)

–0.5

0.05 B´´ (b)

(a)

As

0.00

1.0

1.5

–1.0 –5.0

0.0

0.5 1.0 C-7.0 (d)

1.5

2.0

Figure 7.25  Peak tailing of carboxylic acids and protonated bases as a function of B" or C. (a) Asymmetry factor As for protonated bases and alkylsilica columns (both types A and B) at pH 2.8 versus C-2.8; (b) values of As for benzoic acids and type-B alkylsilica columns at pH 2.8 versus B"; (c, d) values of As for berberine and alkylsilica columns (both types A and B) at pH 7.0 versus values of either C-2.8 or C-7.0. (a, b): adapted from D. H. Marchand et al. 2008. Journal of Chromatography A 1191:2; (c, d): unreported data.

be used to predict peak tailing for bare silica columns used in hydrophilic interaction chromatography (HILIC), as illustrated in Figure 7.26. Here, symmetrical peaks are observed in (a) for C-2.8 = 0.15 (i.e., type-B silica), moderate tailing is seen in (b) for a somewhat higher value of C-2.8 = 0.32, and severe tailing is found in (c) for a clearly type-A silica with C-2.8 = 1.48.

7.4.5  Design of Columns with Unique Selectivity Section 7.3 describes how values of H, S*, etc. for type-B alkylsilica columns depend on various column properties (n, C L , d pore, end-capping), as summarized in Figures 7.6, 7.8, 7.11, 7.14, 7.20, and 7.21. A suitable choice of these column properties might therefore define new type-B alkylsilica columns of preselected selectivity (i.e., chosen values of H, S*, etc.) within some range of attainable © 2012 Taylor & Francis Group, LLC

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(a) YMC Sil C-2.8 = –0.15

(b)

Nucleosil silica C-2.8 = 0.32

(c)

0

Zorbax SIL C-2.8 = 1.48

5

10

15 (min)

Figure 7.26  Tailing of pyrimidines on HILIC columns. Conditions: 250 × 4.6 mm silica columns (YMC SIL, Nucleosil silica, and Zorbax SIL); mobile phase: 75% acetonitrile/buffer (5 mM phosphoric acid); 1.0 mL/min; ambient. Values of C-2.8 were measured for C18 RPC columns from same source (see text for details). (Adapted from B. A. Olsen. 2001. Journal of Chromatography A 913:113.)

values of H, S*, etc. Possibly, this approach can be expanded further by assuming similar changes in values of H, S*, etc. for other column types as column properties are varied. In this way, inherent differences in selectivity for presently available columns (Section 7.3) might be amplified by further changes in column properties. Opportunities for new columns of different selectivity might also be uncovered by considering five-dimensional plots versus H, S*, etc. for all columns with known values of these column parameters. A visual approximation to the latter approach has been described by Zhang and Carr [93], based on the following steps:



1. Express values of the column parameters as ratios versus values of H: XS = S*/H, X A = A/H, etc.; this can be justified on the basis that values of H have only a small effect on selectivity and can therefore be ignored (as well as for other reasons described in reference 93). 2. Define relative parameters χi as values of X over the sum of values of X for three of the four parameters being plotted: for example, χS = XS /(XS + X A + X B) (≡S*/[S* + A + B] for a plot of values of S*, A, and B. 3. Visualize relative column selectivities χi in one of four plots, where each plot maps values of χi for three of the four column parameters.

An example is shown in Figure 7.27 for an S*-B-C-2.8 plot. Most of the columns fall within a narrow range of values (dashed closure within the figure), while some © 2012 Taylor & Francis Group, LLC

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1.0

0.1

0.9

0.2

0.8

0.3

0.7

0.4 C

0.6

0.5

B

0.5

0.6

0.4

0.7

0.3

0.8

0.2

0.9 1.0 0.0

0.1 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0

S

Figure 7.27  Visualization of column selectivity by two-dimensional plots. Example for values of S*, B, and C-2.8 for ~400 different columns of all types. See text for details. (Adapted from Y. Zhang, P. W. Carr. 2009. Journal of Chromatography A 1216:6685.)

columns of quite different selectivity are also apparent (larger data points). A complete picture of column selectivity can be obtained when a plot for S*-B-C as in Figure 7.27 is combined with corresponding plots of S*-A-C, S*-B-C, and A-B-C. Blank regions in these various plots correspond to column selectivities that have not yet been realized and therefore offer opportunities for new columns of different selectivity. While further changes in column selectivity are no doubt both possible and likely, it should be noted that a combination of changes in separation conditions (including the column) provides an adequate variation of selectivity for most applications.

7.4.6  Control of Column Manufacture Despite continuing improvement in column manufacture and reproducibility [25–30], users still rank column reproducibility as their most important concern when selecting a column [94]. Manufacturers employ a variety of tests to ensure batch-to-batch column reproducibility, but the success of such procedures depends on the capture of all applicable solute–column interactions. To the extent that the H-S model achieves this, repeatable values of H, S*, etc. should come close to ensuring reproducible selectivity. An additional advantage of their use in quality control is that deviating values of H, S*, etc. can now be related to changes in column properties (Section 7.3), which should make troubleshooting and correcting repeatability problems more systematic. At the present time, we know of two companies that have incorporated the H-S model into their column research and/or manufacturing departments [49]. © 2012 Taylor & Francis Group, LLC

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Another application of the H-S model in column manufacturing has been described by Ian Chappell of Grace in [49]. Following the development of a preparative separation based on a packing made from spherical silica, a less expensive, irregular-silica packing was needed for large-scale production. The required replacement packing was obtained by varying the ligand concentration CL and mapping resulting values of H, S*, etc. versus CL . In this way it was possible to match values of H, S*, etc. for the irregular-silica packing with values for the original spherical-silica packing. This approach can be expanded to allow the variation of two or more column properties, guided by the data of Figures 7.6, 7.8, 7.11, 7.14, 7.20, and 7.21.

7.4.7  Stationary-Phase Degradation RPC columns undergo changes during use, usually attributed to attack by the mobile phase on the stationary phase. As a result, ligands are detached from the silica surface of the packing, and unreacted silanols are created. This is expected to result in a decrease in column hydrophobicity and an increase in cation-exchange capacity. One study [95] based on a different procedure for characterizing column selectivity has confirmed these trends for both the use and storage of several RPC columns of varying types (types-A and -B alkylsilica, embedded polar group, etc.). The application of the H-S model to several type-B alkylsilica columns [47] found that values of A and C-2.8 increased during the storage of these columns in acetonitrile over a period of 2–27 months. That is, silanols appeared to increase during storage. Both the storage and use of RPC columns appears to result in changes in column selectivity. Further work is needed to better characterize the extent and seriousness of such changes in the column, possibly best guided by changes in H, S*, etc.

7.4.8  Identifying Column Type We have referred to type-A and -B alkylsilica columns, which differ in the kind of silica used to make the starting particles. Type-B silica is prepared by the hydrolysis of tetraalkoxysilanes, which minimizes the presence of contaminating metals in the final silica. Most columns introduced since 1990 are type B because of their generally better performance (reduced peak tailing, better reproducibility). Types-A and -B alkylsilica columns can be differentiated on the basis of their values of C-2.8, as seen in Figure 7.28. Columns with C-2.8 < 0.3 can be assumed to be type B, which agrees with the fact that columns with C-2.8 < 0.3 are less likely to exhibit peak tailing for ionized bases (Figure 7.25a). Other possibilities exist for the identification of column type on the basis of values of H, S*, etc. [46], but appear to be less useful.

7.4.9  Predictions of Retention as a Function of the Column The exceptional accuracy of Equation 7.5 (±1% for values of k) when applied to type-B alkylsilica columns suggests some possible applications. If values of k for the components of a sample could be predicted accurately for different columns, a © 2012 Taylor & Francis Group, LLC

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30

Type-B

C-28 = 0.25

% of Columns

20 10

15 10 5

Type-A

–0.5

0.0

0.5

C-28

1.0

1.5

2.0

Figure 7.28  Distribution of values of C-2.8 for alkylsilica columns. (a) Type B and (b) type A. (Adapted from D. H. Marchand et al. 2008. Journal of Chromatography A 1191:2.)

“best” column could be selected for an improved separation. Alternatively, if retention data exist for a large number of related compounds and some set of separation conditions, predictions of retention for other columns might facilitate peak identification when separation conditions vary among different laboratories. The choice of an “orthogonal” column as in Section 7.3.3 is a step toward selecting a “best” column, but usually a change in just the column does not lead directly to a satisfactory separation; further changes in conditions that affect selectivity are generally required [72]. The selection of a “best” column—or what we refer to as column optimization—would instead rely on the prediction of values of k as a function of the solute and column. A rudimentary form of column optimization has been described, based on the predictable combination of small sections of different columns in series [96]. As an example of what we mean by column optimization, consider the example of Figure 7.29. In an initial separation (Figure 7.29a), anisole (ii) and 5-phenylpentanol (i) are separated on a HiChrom RPB (50% acetonitrile/buffer) with a resolution of Rs = 0.8. Our goal is to find a column that provides maximum resolution of these two solutes, while maintaining other separation conditions the same. Because these two compounds are among the test solutes used to measure values of H, S*, etc. (Appendix 7.1, Table 7.11), their solute parameters η′, σ′, etc. are already known. Consequently, their values of k and retention time can be calculated by means of Equation 7.5 for any column for which we have values of H, S*, etc. (>500 columns). Because such calculations are more accurate for type-B alkylsilica columns, we will limit our search to 258 columns of this kind (a plate number N = 10,000 will be assumed; e.g., a 150 × 4.6 mm column packed with 5 μm particles). Resulting values of R s for the latter 258 columns are summarized in Figure 7.29(b), where only one in seven columns is found to provide an acceptable resolution of Rs ≥ 2. However, a J′Sphere H80 column is predicted to provide a more than adequate resolution of Rs = 4.2 (Figure 7.29c). The example of Figure  7.29 appears encouraging, but its similar application to other separations is limited to (a) the 17 compounds of Table 7.11 (Appendix 7.1), (b) the conditions used for column testing (50% acetronitrile/pH 2.8 buffer, 35°C), and © 2012 Taylor & Francis Group, LLC

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i

0

ii

2 Time (min)

% of Columns

(a) HiChrom RPB

40 30 20 10

J’Sphere H80 0

1

2 Rs

3

4

(b) i

J’Sphere H80 Rs = 4.2 0

2

ii 4

Time (min) (c)

Figure 7.29  Prediction of an optimum column [52]. Sample: 5-phenylpentanol-(i)  and anisole (ii). Conditions: 50% acetonitrile/pH 2.8 buffer; 150 × 4.6 mm columns, 35°C, 2.0 mL/min. See text for details.

(c) isocratic separation. As such, this approach has no practical value. Its extension for a more general and useful procedure requires the measurement of values of η′, σ′, etc. for each sample component under the conditions of the original separation, followed by the application of Equation 7.5 to all columns for which values of H, S*, etc. are known. Preliminary work on such an approach has identified a number of possible problems that might significantly limit the accuracy of final predictions of retention time and resolution. However, even approximate predictions of retention time might be useful in some cases; a related example is the identification of peptide peaks, based on a combination of mass spectrometry and predictions of peak retention by a different procedure [97].

7.4.10  Miscellaneous Other Applications To the extent that values of H, S*, etc. measure fundamental characteristics of a column, various phenomena associated with the column should be more amenable to understanding and control. Two such examples follow. 7.4.10.1  “Slow” Column Equilibration This phenomenon has been encountered with some columns for samples that contain ionized acids or bases [47,98]. For samples free of such components, equilibration of the column after a change of mobile phase usually occurs within a few minutes. © 2012 Taylor & Francis Group, LLC

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1.6 k 1.4

Ami+

1.2 1.0

0

20

Time (min)

40

60

0.2

0.4

(a)

%-Change

0 –2 –4 –6 –0.6

–0.2

C-28 (b)

Figure 7.30  Slow column equilibration for ionized solutes. (a) Retention versus time for an ionized acid (toluene sulfonate, TS –) and base (amitriptyline, Ami+) with a Symmetry C18 column; (b) percentage change in k for amitriptyline (during 1 h) versus C-2.8 for different columns. Conditions: (a) 30% acetonitrile, pH 3.0 buffer, 35°C, 2.0 mL/min, 150 × 4.6 mm columns; (b) same, except 50% acetonitrile, pH 2.8. (Adapted from D. H. Marchand, L. R. Snyder. 2008. Journal of Chromatography A 1209:104.)

Depending on separation conditions (pH, %B, etc.), however, the retention times of ionized solutes may continue to change significantly for anywhere from 1 to 10 h. Cationic solutes show a decrease in retention during equilibration, while anionic solutes exhibit increased retention; see the example of Figure 7.30(a) for separation on a Symmetry C18 column of the fully ionized solutes toluene sulfonate (TS–) and amitriptyline (Ami+). The latter behavior of ionized solutes suggests that the charge on the stationary phase becomes increasingly positive during equilibration. Some type-B alkylsilica columns possess anion-exchange behavior (Section 7.3.4.1), suggesting the presence of positively charged groups within the stationary phase. The presence of such cationic groups in the stationary phase should lead to a lower negative charge and reduced cation-exchange capacity (i.e., lower values of C)—especially at low pH. In agreement with these expectations, the extent of slow column equilibration is observed to increase for more negative values of C-2.8 and becomes insignificant for columns with C-2.8 > 0.0 (for which values of q+ and anion-exchange behavior dissa­ppear; Figure 7.14a). An example is shown in Figure 7.30(b); for the solute amitriptyline and a mobile-phase pH of 2.8, changes in retention over a 50 min interval © 2012 Taylor & Francis Group, LLC

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are plotted versus C-2.8 for several different columns. It is thus possible to anticipate the likely importance of slow equilibration for a column from its value of C-2.8. The scatter of data in Figure 7.30(b) reflects the inexact relationship between the positive charge on the column q+ and values of C-2.8 (see Figure 7.14a). 7.4.10.2  Stationary-Phase “De-wetting” When RPC is used with a near-aqueous mobile phase (>95% water), several problems may be encountered: changes in sample retention with time, decrease in values of N, and long equilibration times when changing from one mobile phase to another. This behavior is the result of stationary-phase de-wetting—sometimes (incorrectly) called “phase collapse”—with the consequent expulsion of mobile phase from the pores of the particle (see Section 5.3.2.3 in reference 72). Column de-wetting is more likely for narrow-pore, more hydrophobic columns—that is, columns with larger values of H. An average value of H = 0.99 is found in Table 7.2(a) for narrow-pore (≤12 nm), type-B C18 columns (the most popular columns), and columns with lower values of H should be less likely to experience column de-wetting. Polar-end-capped columns (average H = 0.90) are specifically designed to minimize column de-wetting, but are otherwise similar to type-B C18 columns in terms of selectivity (because the effect of H on selectivity is less important, as can be seen from the weighting factors in Equation 7.23(a) and Table 7.8). As observed in Figure 7.6, H and stationary-phase de-wetting should also decrease for shorter ligands (Figure 7.6a) and lower ligand concentrations (Figure 7.6c).

7.5  A Comparison of Different Procedures for Describing Column Selectivity While our emphasis in this chapter has been on an understanding and possible uses of the H-S model, a large number of other procedures for characterizing column selectivity have been reported (e.g., references 1–24). Many of these procedures have played an important role in stimulating interest in this area, providing an incentive that has quickened the pace of related research, assisting practicing chromatographers in the selection of the right column, and bringing column characterization into mainstream use. Their practical value over the past two decades has been quite substantial. It is possible that some of these column test methods might prove to be useful complements for the H-S model or even superior in some applications. The present section will therefore attempt to appraise the characteristics of some of these other procedures critically in comparison with the H-S model. Before attempting this, it is worthwhile to consider some requirements of an “ideal” procedure—that is, one that aims at a quantitative understanding of different columns in terms of selectivity—for application to a broad range of related questions (as in Section 7.4): • Allows a quantitative comparison of column selectivity for different samples by means of available software (preferably “freeware”) • Reproducible column-selectivity parameters that are available for a large number of commercial RPC columns • Applicable to different types of RPC columns © 2012 Taylor & Francis Group, LLC

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• Accounts for all solute–column interactions that contribute significantly to selectivity • Column parameters corresponding to specific solute–column interactions • Can relate column selectivity to the composition of the stationary phase • Change in retention for use of a different column can be calculated At the present time, no procedure for characterizing column selectivity fulfills all of these requirements. However, the applications of Section 7.4 do not require all of the features of an “ideal” procedure. For example, if only the first two requirements are met (column-comparison software available with column parameters for about 100 or more commonly used columns), a user can conveniently identify “equivalent” columns for replacement in a routine method application (Section 7.4.2). At the present time, four procedures that meet the latter requirement are available as freeware: the present H-S model, as well as procedures by the US Pharmacopeia [99,100], Katholieke Universiteit Leuven (KUL) [15,101–110], and Euerby et al [5,14,73,83,111– 117]. The column-selectivity parameters reported by the latter three procedures are summarized in Table 7.9 (corresponding to values of H, S*, etc. for the H-S model). A

Table 7.9 Column-Selectivity Parameters Measured by the USP, KUL, and Euerby Procedures Parameter

Column Property Measured USP

k for ethylbenzene TF for quinizarina TF and k for amitriptylinea αTBN/BaPb

Hydrophobicity Chelation ability Silanol activity toward bases Shape selectivity KUL

α(benzylamine/phenol) at pH 2.7 k for 2,2-dipyridyl k for amylbenzene α(triphenylene/o-terphenyl)

Cation-exchange capacity Chelation ability Hydrophobicity Shape selectivity Euerby

α(C5/C4 benzene) α(triphenylene/o-terphenyl) α(caffeine/phenol) α(benzylamine/phenol) at pH 2.7 α(benzylamine/phenol) at pH 7.6

Hydrophobicity Shape selectivity Hydrogen-bond acidity Cation-exchange capacity at ph 2.7 Cation-exchange capacity at ph 7.6

Note: See Table 7.11 for individual test solutes used in the H-S procedure. a TF is tailing factor. b Ratio of k for tetrabenzonaphthalene and benzo[a]pyrene.

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Table 7.10 Comparison of Four Currently Available Column-Characterization Procedures Procedure H-S model USPc Euerby et al.d KULe b

a

b c d e

Meets Requirements for “Ideal” Procedure?a No. 2

No. 3

No. 4

No. 5

No. 6

No. 7

~500 ~100 ~300 ~80

All C18 All C18

Type B only No No No

Yes No No No

Yes No No No

Yes No No No

No. 2: number of columns in database; no. 3: column types in database; no. 4: accounts for all solute-column interactions (type-B alkylsilica columns); no. 5: each solute–column interaction measured (type-B alkylsilica columns); no. 6: column selectivity relatable to stationary-phase composition; no. 7: accurate prediction of sample retention. http://www.USP.org/USPNF/columns.html (PQRI database). http://www.USP.org/USPNF/columns.html (USP database). ACD Labs Column Selector at www.acdlabs.com/products/adl/chron/chronproc http://www.pharm.kuleuven.be/pharmchem/Pages/ccs.html, 2008.

comparison of the latter four procedures with the requirements of an “ideal” method is provided by Table 7.10 and discussed in the remainder of this section. See Table 7.10 for website access to software for the implementation of each of these four procedures.

7.5.1  Number of Columns in the Database (Requirement 2 in Table 7.10) An “ideal” procedure for characterizing column selectivity would have a database that contains selectivity parameters for all RPC columns that are commercially available (~1,000 columns as of this writing [118]). Far fewer columns are necessary for selecting columns of similar or different selectivity, but the greater the number of commonly used columns in the software database, the more widely applicable is the procedure. A larger number of columns makes it more likely that the database will contain information for the column for which a replacement column (of either similar or different selectivity)is desired. More columns also increase the likelihood of finding the best alternate column. Returning to Table 7.10, the four procedures can be ranked as follows in terms of the size of their column databases:

H-S (~500 columns) > Euerby (~300) > USP (~100) ≈ KUL (~80)

7.5.2  Types of Columns in the Database (Requirement 3 in Table 7.10) Two of the procedures of Table 7.10 are limited to C18 columns only (USP, KUL). The H-S and Euerby procedures include examples of most RPC column types that are

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commercially available. Each of the latter two procedures also has data for more C18 columns than are present in either the USP or KUL database. C18 columns account for a significant fraction of all RPC columns in routine use, so a database limited to such columns can still prove useful when seeking a column of similar selectivity. However, when the goal is a column of very different selectivity, the use of columns of different types vastly expands the possible orthogonality of the alternate column [46]. Limiting the search for an orthogonal column to just C18 columns is not likely to be fruitful.

7.5.3  All Solute–Column Interactions Measured? (Requirement 4 in Table 7.10) It is not an easy task to demonstrate that the column-selectivity parameters for a given procedure account for all possible solute–column interactions. If certain interactions are not included in the column-selectivity parameters, it is possible for two columns to appear equivalent in selectivity but give different separations for some samples. We have already noted (Section 7.3.6) that cyano columns are capable of dipole–dipole interaction with the solute, while both cyano and phenyl columns can undergo π–π interactions. No one of the four procedures of Table 7.10 provides for the inclusion of these column properties. On the other hand, these interactions are only significant for a relatively small subset of solutes—and only for phenyl or cyano columns, so they can be ignored in most cases. The H-S model does not measure shape selectivity, but steric interaction is relatively more significant for most samples and columns. For type-B alkylsilica columns, the close agreement of Equation 7.5 for 150 different solutes of widely varying structure suggests that the five solute parameters (H, S*, etc.) do account for all significant solute–column interactions. An associated conclusion is that any procedure for measuring column selectivity must include parameters equivalent to the five parameters of Equation 7.5 (i.e., that measure these five interactions). None of the last three procedures of Table 7.10 measures column H-B basicity, and some of these procedures miss other solute–column interactions as well. The USP and KUL procedures measure “chelation ability,” which is not determined by the other two procedures. As noted earlier, however, chelation is rarely observed—and usually only for type-A columns. The importance of chelation is generally negligible for columns in common use today.

7.5.4  Measurement of Specific Solute-Column Interactions (Requirement 5 in Table 7.10) In the case of the H-S model, its derivation suggests that values of H, S*, etc. measure specific solute–column interactions, whereas in the case of the remaining column test procedures of Table 7.9, there is less basis for assuming that these column parameters correspond in each case to “pure” interactions as opposed to being a composite of more than one interaction. For example, the use of a value of k for a hydrocarbon as a measure of hydrophobicity does not take into account differences in column

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surface area, while measurements of α for two hydrocarbon homologs represent a composite of both hydrophobicity and steric interaction. Similarly, shape selectivity is not the same as steric interaction (Section 7.3.2); the latter is far more relevant for most columns. For some applications, this nonspecificity of the measured column parameters is not critical. Thus, if enough column parameters are determined, even if each parameter represents a composite of more than one interaction, it may still be possible to specify column selectivity uniquely and successfully choose columns of similar or different selectivity. Column parameters that reflect a single interaction are most useful for applications where an understanding of the underlying chemistry is important—for example, in diagnosing problems associated with column manufacture (Section 7.4.6) or interpretations of column degradation (Section 7.4.7).

7.5.5  R  elation of Column Selectivity to Stationary-Phase Composition (Requirement 6 in Table 7.10) Establishing the dependence of each column parameter on stationary-phase chemistry and column properties can prove useful in different ways: design of new columns of different selectivity (Section 7.4.5), column manufacturing (Section 7.4.6), etc. Figures 7.6, 7.8, 7.11, 7.14, 7.20, and 7.21 describe the dependence of values of H, S*, etc. on such column properties as ligand length, ligand concentration, pore diameter, and end-capping. No similar data have been reported for the other three procedures of Table 7.10.

7.5.6  Predictions of Retention The H-S model is the only procedure so far reported that seems capable of accurate predictions of solute retention as a function of the column. This may eventually lead to some practical applications, as suggested in Section 7.4.5.

7.5.7  Summary Table 7.10 and the preceding discussion summarize some of the advantages of the H-S model for different applications of column-selectivity parameters. A possible disadvantage has been claimed for the application of this model [110]—namely, that the H-S column test procedure is “complicated and difficult to perform.” When the columns of interest are already in the H-S database, this concern should apply only minimally, if at all. The large (and increasing) size of this database makes it unlikely that a user will need to measure values of H, S*, etc. for a given column. In any case, the H-S test procedure is reasonably straightforward to carry out (Appendix 7.1), and any increased effort relative to the other three procedures of Table 7.10 must be weighed against the intended use of resulting data (as summarized in Table 7.10).

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7.6  Conclusions The present chapter summarized the further development and application of the hydrophobic-subtraction (H-S) model of RPC selectivity, which relates solute retention k to various solute-stationary phase interactions:

log k = log kEB + η′H – σ′S* + β′A + α′B + κ′C



(i)

(ii)

(iii) (iv)

(7.5, from Section 7.2.1)

(v)

It is believed that the five terms of Equation 7.5 account for all of the solute–column interactions that occur in RPC separations with monomeric type-B alkylsilica columns: hydrophobicity (i), steric interaction (ii), hydrogen bonding between an acceptor solute and a silanol (iii) or between a donor solute and an acceptor entity within the stationary phase (iv), and cation exchange or other ionic interactions (v). The role of the solute is represented by parameters η′, σ′, etc., while the column is characterized by parameters H, S*, etc. The H-S model can be extended to other kinds of columns (e.g., type-A alkylsilica, phenyl, cyano, etc.), but with poorer accuracy in the application of Equation 7.5 (largely as a result of term iv). We believe that each term of Equation 7.5 corresponds to a single (“pure”) interaction, rather than a mixture of two or more different interactions. Assuming that this is the case, values of the solute and column parameters for each interaction can be compared with solute molecular structure and column properties such as ligand length and coverage, pore diameter, and end-capping with two goals in mind. First, these comparisons should make sense in terms of what we know about the general nature of each interaction, hence testing the validity of the H-S model. Second, such an analysis can provide additional insight into individual solute–column interactions. The present summary (Section 7.3) describes what has so far been achieved by comparisons of this kind. In many respects, however, a thorough understanding of these solute–column interactions remains out of reach because of the complexity of the RPC retention process. The nature of steric interaction is now better understood and appears largely consistent with experimental data (Section 7.3.2). Differences between steric inte­ raction and shape selectivity have been more clearly defined. While term iv of Equation  7.5 (hydrogen bonding between acidic solutes and basic columns) is incorporated into the solvation equation (term iv of Equation 7.1), no previous work had demonstrated its significance in separations by reversed-phase chromatography. However, the nature of term iv (Section 7.3.5.) remains somewhat puzzling, in that our results show marked inconsistencies with similar interactions in solution. These observations may eventually provide a basis for new insights into the nature of this interaction; alternatively, our interpretation of term iv may have missed the mark in some way. There is strong evidence that at least two ionic groups in the stationary phase (one positive and the other negative) contribute to column cation-exchange capacity

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C at low pH (at least for some columns). Ionized silanols could provide the negative charge, but end-capping the column has little effect on values of C at low pH, which raises possible questions about the role of silanols in this connection. Several applications of the H-S model have now been demonstrated, and other uses of the model are suggested by the apparently fundamental nature of the column parameters H, S*, etc. (Section 7.4). A number of other procedures for characterizing column selectivity have been reported, usually for the purpose of choosing a column of either similar or different selectivity. Three of the more useful of these procedures have been reviewed and compared with the H-S model (Section 7.5).

Acknowledgments The authors much appreciate the considerable assistance provided by the following reviewers of the manuscript: Dr. David McCalley (University of the West of England), Dr. Mel Euerby (HiChrom Ltd.), and Dr. Uwe Neue (Waters Corp). The authors also wish to dedicate this chapter to the memory of Dr. Uwe Neue (deceased), an outstanding scientist who made numerous contributions to the field of chromatography during his unfortunately short lifetime. Uwe was part of a small group who contributed to the initial planning of research on what eventually became the hydrophobic-subtraction model. Over the next dozen years, he offered many important suggestions that helped guide the project to a successful conclusion, as well as coauthored two recent publications [50,51]. His review of this chapter was carried out during his final days, which to us represents a remarkable example of his great dedication and sense of responsibility. He will be missed.

Appendix 7.1: Routine Measurement of ColumnSelectivity Parameters H, S*, A, B, and C A conventional HPLC system can be used for the following column-test procedure. As the hold-up volume of the system is cancelled by the calculation [31], the hold-up volume can be ignored. If online mixing is used, the system should be calibrated to deliver 50 ± 0.1% v/v of the B-solvent (acetonitrile). A column for testing is first flushed with pH 2.8 mobile phase (50% v/v acetonitrile/buffer; the buffer prior to mixing with acetonitrile is 60 mM potassium phosphate; pH 2.80), capped off (static equilibration), and stored at ambient conditions for 8–16 h. Aqueous buffers are prepared by weight (see Appendix 7.2 of reference 72) and checked by pH meter. Following static equilibration, the column is connected to the HPLC system and mobile phase flow is begun. After 20 min, 10 μL of each of the seven samples of Table 7.11 (mixtures 1 through 4) are successively injected at 10 min intervals. Repeat injections of amitriptyline and nortriptyline are made after the injection of mixture 4, and the column is stored in 50% v/v acetonitrile/water.

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Table 7.11 Samples Used for H-S Column Test Procedure η′

σ′

β′

α′

κ′

Mix 1:  Thioureaa Amitriptylineb (no. 1) n-Butylbenzoic acid (no. 2)

— –1.094 –0.266

— 0.163 –0.223

— –0.041 0.013

— 0.300 0.838

— 0.817 0.045

Mix 1a:  N,N-diethylacetamide (no. 3) 5-Phenylpentanol (no. 4) Ethylbenzene (no. 5)

–1.390 –0.495 0

0.214 0.136 0

0.369 0.030 0

–0.215 0.610 0

0.047 0.013 0

Mix 2:  N,N-dimethylacetamide (no. 6) 5,5-Diphenylhydantoin (no. 7) Toluene (no. 8)

–1.903 –0.940 –0.205

0.001 0.026 –0.095

0.994 0.003 0.011

–0.012 0.568 –0.214

0.001 0.007 0.005

Mix 2a:  Nortriptyline (no. 9) Acetophenone (no. 10) Mefenamic acid (no. 11) Mix 3:  4-Nitrophenol (no. 12) Anisole (no. 13) Mix 3a:  Benzonitrile (no. 14) cis-Chalcone (no. 15) trans-Chalcone (no. 16) Mix 4:  Berberineb (no. 17)

–1.163 –0.744 0.049 –0.968 –0.467 –0.703 –0.048 0.029 —

–0.018 0.133 0.333 0.040 0.062 0.317 0.821 0.918 —

–0.024 0.059 –0.049 0.009 0.006 0.003 –0.030 –0.021 —

0.289 –0.152 1.123 0.098 –0.156 0.080 0.466 –0.292 —

0.845 –0.009 –0.008 –0.021 –0.009 –0.030 –0.045 –0.017 —

Solute

Note: Each solute is present in a concentration of ~50 mg/mL. A 10-μL injection is made of each mix. a Used as dead-time number to calculate values of k. b Measured at both pH 2.8 and 7.0.

At a later time, the column is reinstalled for testing with pH 7.0 mobile phase (50% v/v acetonitrile/buffer; buffer is pH 7.00, 60 mM potassium phosphate). After 20 to 40 min of flow of mobile phase through the column, mix 4 is injected three times at 20 min intervals. Other experimental conditions (and their required repeatability) are given in Table 7.2. The solutes of Table 7.11 are commercially available, except for cis-chalcone. The latter can be prepared from trans-chalcone by exposing a solution of the latter to sunlight or UV light, which yields a mixture of cis and trans isomers for use in mixture 3a (the cis isomer is always less retained than the trans). For each mixture in Table 7.11, compounds normally elute in the order shown (e.g., for mixture 1, peaks would elute in the order of 1, 2, and 3). Occasionally it will be found that amitriptyline and/or nortriptyline will elute later than other compounds in mixtures 1 and 2a, so their retention times should be compared with values for the pure compounds (last two injections at pH 2.8). Because of the possibility of slow column equilibration (Section 7.4.10), the retention times for different injections of these two compounds should be compared; retention

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times should not vary by more than 1%. Very occasionally, amitriptyline and/or nortriptyline will elute before thiourea. When this occurs (due to cation exclusion from positively charged columns), the retention time of the solute is set to that of thiourea plus 0.01 min (a large SE for the regression can then be anticipated). Apart from the case of amitriptyline and nortriptyline, it is possible (but not likely) for other solute pairs to change positions or to merge into a single peak. Peak areas can be used to resolve which peak is which. When peak inversions occur and are initially overlooked, the SE for the regression (described later) will usually exceed the values of Table 7.2 by several-fold. Consequently, when unusually large SE values are encountered, the possibility of peak inversion should be investigated. Retention times tR for compounds 2–15 are next converted to values of k = (tR – t0)/ t0, where t0 = tR for thiourea. Values of α equal to k for each solute divided by k for ethylbenzene are next calculated and then all values of log α are regressed versus the values of η′, σ′, etc. in Table 7.11 (Equation 7.5) to give values of H, S*, etc. for the column. A value of C-7.0 is then calculated from Equation 7.6, using the retention of the quaternary-ammonium compound berberine at pH 2.8 and 7.0. See references 34 and 37 for further details.

Appendix 7.2: Dependence of Column Selectivity on Column Properties The regression statistics for the application of Equation 7.9 to each column parameter are summarized in Table 7.12. The latter values were used to calculate the plots of Figures 7.6, 7.8, 7.11, 7.18, 7.20, and 7.23. These regressions capture only a fraction of the total variance, equal to resulting values of r 2 (third row of Table 7.12). It was noted in Section 7.3 that much of the remaining variance can be explained by differences in the silica used to prepare the column packing (and also its pretreatment), as well as other changes in the manufacturing process that can affect retention (e.g., type of silane and end-capping reagent, other differences in reaction conditions, etc.). This conclusion is justified next, with values of the residual unexplained variance listed in the last row of Table 7.12. If we consider matched columns that differ only in the ligand—for example, Symmetry C18 versus Symmetry C8 —the use of the same silica and a similar manufacturing process seems likely for many (but not necessarily all) such column pairs. We can use values of H as an example for each of the column parameters. The effect of these added contributions to values of H (apart from column properties n, CL , d pore, end-capping) can be examined by means of the quantity δH, equal to the experimental value of H minus the value calculated from Equation 7.9 (i.e., the error in calculated values of H). We might expect similar values of δH for each of two such matched columns because whatever contributes to H beyond the variables of Equation 7.9 should be similar for each column (assuming the same silica and similar manufacturing conditions), resulting in similar values of δH and a near-zero value of ΔδH (the difference between the two values of δH) as well as SD = 0 for two δH values. © 2012 Taylor & Francis Group, LLC

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Table 7.12 Summary of Regression of Column Parameters versus Properties (Equation 7.9) Number of Omitted Columnsa r2 Std. error (SE) a (intercept) b (ligand length n) c (n2) d (pore diameter dpore) e (dpore2) f (bonding concentration CL) g (CL2) h (end capping) Unexplained variancec a

b c

H 24

S* 11

A 9

B 6

C-7.0 14

C-2.8 3b

0.927 0.031 0.529 0.042 –0.001 –0.011 0.000 0.044 –0.003 0.033 1%

0.775 0.019 –0.165 0.009 0.000 –0.002 0.000 0.031 –0.002 0.067 3%

0.685 0.078 –0.173 0.031 –0.001 –0.010 0.000 0.072 –0.006 –0.321 4%

0.620 0.014 0.007 –0.003 0.000 0.006 0.000 –0.008 0.001 –0.012 6%

0.666 0.163 1.065 –0.026 0.001 –0.005 0.000 –0.065 0.005 –0.670 7%

0.630 0.048 –0.149 0.004 0.000 0.013 0.000 0.022 –0.001 –0.026 11%

Columns with values of H, S*, etc. from Equation 7.9 that deviate by >2.7 SE were omitted from the correlation. But excluding 58 additional columns with C-2.8 < 0. Determined as described in Appendix 7.2.

There are 30 pairs of matched columns among the 167 columns under study, for each of which pairs we can determine the standard deviation SD for their δH values. In the absence of any similarity of a C8 versus a C18 column, as two columns are involved in the calculation of δH, a value of SD(δH) should equal 21/2 times the SD value of Table 7.12; that is, 21/2 × 0.0312 = 0.0441. If certain contributions to H (other than those predicted by Equation 7.9) are similar for matched columns, actual values of SD(δH) should be generally smaller than 0.0441. This prediction is tested in Figure 7.31(a) as a frequency plot of values of SD(δH) for matched columns. As expected, the majority of column pairs (25) have SD(δH) 0.044 in Figure 7.31(a) are also not unexpected. A cluster of outliers is seen in Figure  7.31(a), with SD > 0.044. Presumably, these column pairs have indeed experienced greater differences in their preparation. With the exclusion of these five outliers, the average value of SD for the remaining 25 column pairs is only 0.014. Because the variance in uncorrected values of H is SD = 0.133, the unexplained variance in H is then (0.014/0.133)2, or just 1%. A similar approach can be used for the remaining column parameters, as shown in Figure 7.31(b–f). Values of the unexplained variance for each column parameter are shown in the last line of Table 7.12. For further details, see references 50 and 51.

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H

1.41 × SE Eqn. 7.9

4 2 0.02

0.00

0.04

0.06 SD for δH

0.08

0.10

(a) 8 6 4 2

S*

1.41 × SE Eqn. 7.9

0

0.01

0.02

0.03 SD (δS*)

0.04

0.05

(b)

# of Columns

8 6 4 2

1.41 × SE Eqn. 7.9

0

0.05

A

0.10

SD (δA)

0.15

(c) 6

B

1.41 × SE Eqn. 7.9

4 2 0.004

0.008

0.012 SD for (δB)

0.016

0.020

(d)

8 6 4 2

1.41 × SE Eqn. 7.9

0.02

0

0.04

0.06 SD (δC-2.8)

C-2.8

0.08

0.10

(e) 10 8 6 4 2

1.41 × SE Eqn. 7.9 0

0.05

0.10

0.15

0.20 0.25 SD (δC-7.0)

0.30

0.35

C-7.0

0.40

(f )

Figure 7.31  Origin of unexplained contributions to (a) H; (b) S*; (c) A; (d) B; (e) C-2.8, and (f) C-7.0 (as shown by “matched” C8 and C18 columns [50,51].

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Symbols a A A b A1, A2 b B B′′ Bb B1, B2 C C-2.8 C-7.0 C-x Cb C L C1, C2 c(NO3 –) d dpore EPG Fs H H b H-B H-S H1, H2 k kEB k x, k7.0 L L/W M n n′ Po/w

stationary phase hydrogen-bond basicity (Equation 7.1); also, a constant “type-A” column made from metal-containing silica; also, column hydrogenbond acidity, related to number and accessibility of silanol groups in the stationary phase (Equation 7.5) average value of column H-B acidity A for type-B alkyl-silica columns (Equation 7.22) values of H-B acidity A for columns 1 and 2 stationary phase hydrogen-bond acidity (Equation 7.1); also, a constant “type-B” column made from pure silica; also, column hydrogen-bond basicity (Equation 7.5) “excess” column basicity (Equation 7.23) average value of column basicity B for type-B alkyl-silica columns (Equation 7.22) values of B for columns 1 and 2 relative column cation-exchange activity, related to number and accessibility of ionized groups within the stationary phase (Equation 7.5) value of C for pH = 2.8 value of C for pH = 7.0 value of C for pH x (Equation 7.6) average value of C for type-B alkyl-silica columns (Equation 7.22) ligand concentration (micromoles per square meter) (Equation 7.9) values of C for columns 1 and 2 slope of a plot of k versus 1/(buffer concentration) for NO3– as solute slope of log k versus buffer cation concentration M (Equation 7.19) pore diameter (nm) (Equation 7.9) embedded or end-capped polar group column-matching function (Equation 7.21a) relative column hydrophobicity (Equation 7.5) average value of H for type-B alkylsilica columns (Equation 7.22) hydrogen bond hydrophobic subtraction values of H for columns 1 and 2 retention factor, equal to (tR–t0)/t0 value of k for ethylbenzene (Equation 7.5) values of k for berberine at pH x and 7.0, respectively (Equation 7.6) molecular length; the number of atoms (excluding hydrogen) in the longest connected series that does not double back on itself (Section 7.3.2) length-to-width ratio of a solute molecule buffer concentration (moles per liter); usually M = [K+] length of a stationary-phase ligand (e.g., n = 18 for C18); also, number of items in a group number of carbons in an alkyl group attached to solute molecule (e.g., Figure 7.10a) octanol–water partition coefficient (Equation 7.8)

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stationary phase excess molar refraction (Equation 7.1); also, correlation coefficient r 2 coefficient of determination R2 solute excess molar refraction (Equation 7.1) RPC reversed-phase chromatography s dipolarity/polarizability parameter for stationary phase (Equation 7.1) S* relative steric resistance to insertion of bulky solute molecules into the stationary phase; as S* increases, bulky solute molecules experience greater difficulty in penetrating the stationary phase and being retained (Equation 7.5) Sb average value of S* for type-B alkylsilica columns (Equation 7.22) S*1, S*2 values of S* for columns 1 and 2 SD standard deviation SD(δH) standard deviation of values of δH (see Appendix 7.2); values of SD(δS*), SD(δA), etc. are defined similarly SE standard error t0 column dead time (min) tR retention time (min) Vx solute molar volume (Equation 7.1) α separation factor for two solutes (the ratio of their k-values) α′ solute hydrogen-bond acidity (Equation 7.5) αT/O ratio of k-values for triphenylene versus o-terphenyl αTBN/BaP ratio of values of k for tetrabenzonaphthalene and benzo[a]pyrene αH2  solute hydrogen-bond acidity in solution (Equation 7.1) β′ solute hydrogen-bond basicity (Equation 7.5) β2 solute hydrogen-bond basicity in solution (Equation 7.1) δH error in a value of H calculated from Equation 7.9; values of δS*, δA, etc. are defined similarly δ log k contribution to log k other than hydrophobicity; see Figure 7.2(b) and related text ΦSS log(1/αTBN/BaP); a measure of shape selectivity that is comparable to S* for steric interaction η′ solute hydrophobicity (Equation 7.5) κ′ charge on solute molecule (positive for cations, negative for anions) (Equation 7.5) κ′i, κ′j values of κ′ for solutes i and j (Equation 7.4a) πH2 dipolarity/polarizability parameter for solute (Equation 7.1) σ′ steric resistance of solute molecule to penetration into stationary phase (σ′ is larger for more bulky molecules) (Equation 7.5) ν free energy to create a cavity in the stationary phase (Equation 7.1) r

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108. E. Haghedooren, K. Koczian, S. Huang, S. Dragovic, B. Noszal, J. Hoogmartens, E. Adams. 2008. Journal of Liquid Chromatography 31:1081. 109. E. Haghedooren, E. Farkas, A. Kerner, S. Dragovic, B. Noszal, J. Hoogmartens, E. Adams. 2008. Talanta 76:172. 110. S. Dragovic, E. Haghedooren, T. Nemeth, I. M. Palabiyik, J. Hoogmartens, E. Adams. 2009. Journal of Chromatography A 1216:3210. 111. M. R. Euerby, C. M. Johnson, I. D. Rushin, D. A. S. S. Tennekoon. 1995. Journal of Chromatography A 705:219. 112. M. R. Euerby, P. Petersson. 2000. LCGC 13:665. 113. M. R. Euerby, A. P. McKeown, P. Petersson. 2003. Journal of Separation Science 26:295. 114. M. R. Euerby, P. Petersson. 2005. Journal of Chromatography A 1088:1. 115. M. R. Euerby, P. Petersson. 2005. Journal of Separation Science 28:2120. 116. M. R. Euerby, P. Petersson. 2006. In HPLC Made to Measure, ed. S. Kromidas, 264– 279. Weinheim, Germany: Wiley-VCH. 117. P. Petersson, M. R. Euerby. 2007. Journal of Separation Science 30:2012. 118. R. E. Majors. 2010. LCGC Supplement 28 (4S): 8.

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Chromatographic Hydrophobicity Index (CHI) Martí Rosés, Elisabeth Bosch, Clara Ràfols, and Elisabet Fuguet

Contents 8.1 Introduction................................................................................................... 377 8.1.1 HPLC Determination of Lipophilicity.............................................. 378 8.1.2 The φ0 Descriptor of Lipophilicity.................................................... 379 8.1.3 The Chromatographic Hydrophobicity Index.................................... 380 8.1.4 Experimental Determination of CHI................................................. 381 8.2 Linear Solvation Energy Relationships and Comparison to Other Lipophilicity Scales............................................................................. 385 8.2.1 Linear Solvation Energy Relationships............................................. 385 8.2.2 Comparison to Isocratic HPLC Retention......................................... 387 8.2.3 Comparison to Other Hydrophobicity Parameters............................ 389 8.3 Determination of CHI for Ionizable Compounds.......................................... 393 8.3.1 Relationship between CHI and pH.................................................... 393 8.3.2 CHI versus pH Profiles for Monoprotic Neutral Compounds........... 395 8.3.3 CHI versus pH Profiles for Polyprotic Compounds...........................405 8.4 Applications in Biological Processes.............................................................408 8.5 Conclusion..................................................................................................... 410 Acknowledgment.................................................................................................... 410 References............................................................................................................... 410

8.1  Introduction It is generally accepted that any pharmacological process occurs in three conceptual steps: penetration, binding, and activation [1]. Hence, to be efficient, it is crucial that a new molecule with potential pharmacological activity possesses adequate abilities to gain access to the biological system, to bind to the biological target and, finally, to achieve a biological response from the formed adduct with an observable effect. Accordingly, the knowledge of certain physicochemical properties is of the utmost importance in the screening processes of new potential drugs. Lipophilicity determines the ability to penetrate a biological membrane. Acidity affects passive transport 377 © 2012 Taylor & Francis Group, LLC

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across the membrane because only the neutral or the ionic form of the drug is active in the living organism. Solubility influences the absorption of orally administrated drugs from the gastrointestinal tract. Since these properties, among others such as the permeability through membranes, significantly influence the ADMET behavior of the molecules (absorption, distribution, metabolism, excretion, and toxicity), the estimation of them in an early stage of the drug discovery process provides extremely useful information to anticipate their feasibility as drug-like candidates [2]. Thus, the literature provides continuously new approaches to determine efficiently the mentioned properties in high-throughput ways, as required by the pharmaceutical laboratories.

8.1.1  HPLC Determination of Lipophilicity One of the most important ADMET properties is lipophilicity (or hydrophobicity), which is commonly expressed as the logarithm of the n-octanol/water partition coefficient (log Po/w) [3]. Different well known experimental approaches to determine it lead to reliable results, but most of them show significant drawbacks. Thus, the classical procedure, taken as the reference one, is the shake-flask method [4], which involves the control of many experimental details when accuracy is required and is highly time consuming. Potentiometric methods offer accurate results but are appropriate only for acidic or basic compounds [5,6]. Both approaches demand significant amounts of high-purity sample. Nowadays, reversed-phase high-performance liquid chromatography (RP-HPLC) is considered one of the best techniques for estimating log Po/w values, due to its highthroughput, insensitivity to impurities or degradation products, broader dynamic range, online detection, and reduced sample size. Most of the published RP-HPLC methods involve the preparation of a robust calibration curve from retention data of several standard compounds with known log Po/w values. The log Po/w of new compounds should be determined by interpolation in the calibration line. Thus, different columns, mobile phases, and mobile phase additives and isocratic or gradient modes have been proposed with diverse success [7–18]. However, it should be noticed that published methods are often restricted to a certain chemical family of compounds or to a limited log Po/w range. Corrections of the retention parameters by means of molecular descriptors of the compounds to estimate log Po/w values have been proposed too [19]. Lipophilicity indexes obtained by HPLC are usually derived from the logarithm of retention factors, log k. In fact, isocratic log k values become a relative scale of lipophilicity, but most researchers [8–12,14–17] prefer working with retention factors extrapolated to pure water (log k w) to obtain more comparative values avoiding the effect of changing the organic modifier. Extrapolated log k w values are obtained from linear or quadratic plots of log k versus the volume fraction of organic modifier in the mobile phase, φ; the linear ones are the most common approaches for the sake of simplicity:

log k = –Sφ + log k w

(8.1)

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where S is the slope of the correlation, which stands for the log k variation caused by changing the organic phase concentration in the mobile phase by 1% [20]. Frequently, the log k versus φ linear plots present deviations at high organic modifier fractions. From a practical point of view, this means that different log k w values can be obtained for the same solute, column, and instrument if different organic modifiers or mobile phase compositions are used. Thus, working in the linear part of the plot is compulsory to minimize error in log k w estimation [12,17,21]. Some studies relate extrapolated log k w to log Po/w values, obtaining good correlations for several sets of compounds via linear regression [7–12,14] and therefore show a convenient way to estimate the n-octanol/water distribution coefficient of organic compounds from the accurate determination of the log k w quantity. In any case, the main limitation of these methods is the accuracy of log k w values, which are strongly conditioned by the experimental conditions of chromatographic measurements; therefore, a careful selection of working conditions is required. For instance, the addition of n-octanol to the mobile phase [8–12] is used to improve the correlation between log Po/w and log k w values compared to that from experiments without n-octanol addition.

8.1.2  The φ 0 Descriptor of Lipophilicity Derived from Equation (8.1), another useful lipophilicity parameter, φ0, was established by Valkó and Slégel [20]. This parameter stands for the organic modifier fraction (methanol or acetonitrile) that produces an equal molar distribution between the stationary and mobile phases in order to obtain log k = 0; that is, it accounts for a retention time exactly double that of the dead time. Then, φ0 is obtained by the following expression:



ϕ0 =

log k w S

(8.2)

where S has been already defined. The higher the φ0 value is the more hydrophobic is the compound. It was also demonstrated that the value of φ0 is characteristic for a given compound and depends only on the type of the organic modifier, pH, and temperature of the mobile phase. It is independent of the reversed-phase column type and length, flow rate, and the mobile phase compositions where the actual retention measurements are carried out. Because of the physical meaning of the φ0 parameter, it becomes a very attractive lipophilicity index since, for most compounds, it is an attainable volume percentage of organic component in the mobile phase with a value between 0 and 100. In addition, the φ0 values obtained with methanol and with acetonitrile showed an excellent correlation with each other. However, only a fair correlation was found between the φ0 values and log Po/w for a set of 140 structurally different compounds when acetonitrile was the organic modifier (r = 0.88; s =12.8) and for a set of almost 500 drug molecules with methanol as the organic component and a pH of the buffered mobile phase that assures the suppression of the ionization of compounds

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(r = 0.787; s = 13.48). Then, φ0 is a good indicator of the relative lipophilicity of organic compounds but just a fair estimator of their log Po/w since it cannot be expected that reversed-phase chromatographic partition coefficients be able to model properly a partition system such as n-octanol/water for structurally unrelated compounds [20]. The main disadvantage for the adoption of φ0 parameter as a lipophilicity index in routine work is that its determination requires too much experimental time and effort and, then, it cannot be considered a high-throughput index.

8.1.3  The Chromatographic Hydrophobicity Index Based on the φ0 parameter, a new index obtained by fast gradient RP-HPLC, named chromatographic hydrophobicity index (CHI), was proposed by Valkó, Bevan, and Reynolds [22]. Since a linear gradient increasing the organic component concentration implies that any point of the run time is equivalent to a certain mobile-phase composition, it is possible to estimate the organic fraction in the mobile phase, φ value, when the compound is eluting from the column, provided the void and dwell volumes are known. Considering a fast gradient run, the S parameter (see Equation 8.1) will only have a small influence on the gradient retention time of the compounds and, therefore, it can be considered constant for each molecule. When applying a fast gradient, it is assumed that lipophilic compounds will bind to the lipophilic stationary phase at the top of the column. They start moving with the mobile phase only when the appropriate concentration of the acetonitrile is achieved depending on their φ0 value. Therefore, it can be assumed that each compound is running with the unretained peak volume when the appropriate organic-phase concentration reaches the top of the column. With these assumptions, the retention time in a fast gradient run should be linearly related to φ0. This hypothesis was tested from the retention of a set of 76 structurally unrelated compounds with calculated log Po/w values between –0.45 and 7.3. These substances were isocratically chromatographed using various volume fractions of acetonitrile in the mobile phase, preferably bracketing the retention when log k was close to zero, that is, the retention time was around twice the dead time. Their isocratic hydrophobicity indexes, φ0, were calculated by means of Equations (8.1) and (8.2). The gradient retention times, tg, were measured under a fast gradient that included a 9 min linear acetonitrile gradient from 0% to 100%. It should be pointed out that the aqueous fraction of the mobile phase was buffered by ammonium acetate (pH ranging from 7.0 to 7.3) but, to keep the compound in the neutral form, in some cases the pH was adjusted to about 2 or about 10, adding formic acid or ammonium hydroxide solutions, respectively. As expected, an excellent correlation between φ0 and tg was found, providing experimental confirmation that a linear fast gradient retention time can be used as a measure of compound hydrophobicity:

φ0 = 14.34 tg – 58.32 n = 76,  R = 0.974,  s = 5.3,  F = 1371

(8.3)

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Table 8.1 Compounds of the Calibration Mixture and Their CHI Values Obtained from 2 × 7 Measurements with Two HPLC Systems Compound Theophylline Phenyltetrazole Benzimidazole Colchicine 8-Phenyltheophylline Acetophenone Indole Propiophenone Butyrophenone Valerophenone

CAS 58-55-9 18039-42-4 51-17-2 64-86-8 961-45-5 98-86-2 120-72-9 93-55-0 495-40-9 1009-14-9

c log Po/w –0.05 1.42 1.55 0.92 2.05 1.66 2.14 2.20 2.73 3.26

CHI 15.76 ± 0.8 20.18 ± 0.7 30.71 ± 0.4 41.37 ± 0.4 52.04 ±0.4 64.90 ± 0.2 69.15 ± 0.2 78.41 ± 0.1 88.49 ± 0.1 97.67 ± 0.3

Note: The CHI values were calculated by means of the slope and intercept of Equation 8.3 (derived from 76 compounds).

The slope and intercept of Equation (8.3) can be used to convert the measured gradient retention time of any organic compound to its CHI value. This approach puts CHI and φ0 on the same scale; that is, the CHI value for a compound approximates to the volume percentage of acetonitrile required to achieve an equal distribution between the mobile and the stationary phases. Several gradient profiles were tested for a smaller subset of compounds, and it was found that a slightly better correlation coefficient was obtained by increasing the gradient speed. Valkó et al. [22] proposed a group of 10 compounds whose CHI parameters were properly determined as the calibration set to standardize a new chromatographic system to be used for further determination of CHI values at pH 7.4. The standard set covers the log Po/w range from −0.02 to 3.26 and is shown in Table 8.1. It should be noticed that these compounds are not ionized at pH 7.4, so their distribution coefficient corresponds to that of the neutral form of each compound. Figure  8.1 depicts the linear relationships between φ0 and experimental tg, showing slope and intercept values very close to those of Equation 8.3. This result confirms that selected compounds are representative of the whole set of 76 substances studied.

8.1.4  Experimental Determination of CHI For setting up the CHI method on a new column or new instrument or with a different mobile phase, the following procedure is suggested. First, measure the linear gradient retention times for each component of a mixture of the 10 selected compounds listed in Table 8.1 on the new reversed-phase system. The linear range of the

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60 50 40 30 20 10 0 5.474

6.474

7.474

8.474 9.474 tg Measured

10.474

11.474

Figure 8.1  Isocratic φ0 values against gradient retention times the for the standard compounds: φ0 = 14.00 tg – 55.9 (n = 10, R = 0.992). (From Valkó, K. et al., 1997, Analytical Chemistry 69:2022–2029.)

gradient from 0% to 100% organic phase could be between 2 and 10 min, depending on the dimensions of the column and the flow rate. Then, perform a linear regression between the measured retention times and the CHI values (Table 8.1) of the test compounds to obtain the coefficients A and B of the following equation:

CHI = A tg + B

(8.4)

Keeping the conditions the same as those used for the test mixture, the CHI value of a new compound can be calculated from its tg and the A and B coefficients. The authors claim that a column can be used for several days without the calibration changing significantly. However, a mixture containing all the calibration set compounds should be injected at regular time intervals, and recalibration should be performed if the retention time differences of the standard compounds are higher than 0.1 min. This calibration procedure is suitable for any reversed-phase HPLC system. Nevertheless, if a column other than ODS should be used, the appropriate isocratic φ0 values will need to be determined again for the calibration compounds in order to align the CHI and φ0 scales as closely as possible. At this point, CHI can be considered a high-throughput chromatographic hydrophobicity index that can be determined for any compound from any reversed-phase chromatographic system. However, as expected, CHI is just a fair estimator of log Po/w values for structurally unrelated compounds, as shown in Figure 8.2. The CHI values obtained for a compound will depend on the type of stationary phase, type of organic modifier (acetonitrile or methanol), and, for acidic or basic compounds, the pH of the mobile phase. Nevertheless, the preceding discussion takes place under the hypothesis that compounds keep to their neutral form during the chromatographic run and this was the reason for using mobile phases buffered at neutral pH with ammonium acetate (pH ≈ 7.4). © 2012 Taylor & Francis Group, LLC

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clogP

5 4 3 2 1 0 –1

0

30

50

CHIN

70

90

110

Figure 8.2  Relationships between the ClogP and the CHIN values. (From Valkó, K. et al., 1997, Analytical Chemistry 69:2022–2029.)

However, since the pH value that assures the presence of only the neutral form depends on the compound pKa, the authors propose mobile phases buffered at acidic or basic pH according to the nature of compounds to be studied. Therefore, as a routine practice, each compound should be chromatographed using acidic, neutral, and basic mobile phases to determine the CHI parameter of the neutral species, CHI value, which is taken as the highest value among those derived from the three mobile phases employed. A deeper discussion about this point is given later in this review. The originally developed CHI method provides gradient retention times based on UV detection, which are converted into CHI values after proper calibration of the chromatographic system. According to the recommended procedure, which involves three chromatographic runs with mobile phases of different pH, one compound can require about 24 min when 8 min gradients are programmed. In order to improve the throughput of the CHI screening, Camurri and Zaramella [23] proposed the use of an LC/MS approach as an extension of the LC/UV original procedure. This new approach allows simultaneous injection of N compounds into the LC/MS system, and the retention time of each compound is extracted from the reconstructed selected ion recording (SIR) chromatograms. The number of SIR traces is limited by the instrument configuration used. Thus, the throughput of the original screening LC/UV method could be in­c­ reased by N times and only three runs are needed to determine the CHI parameter at three different pH values for a set of N compounds, which must have different molecular masses. The highest value of N depends on the total number of channels that can be monitored simultaneously. In the same way, the complete calibration of the chromatographic system requires only three chromatographic runs. Thus, an aliquot of a mixture of the standard compounds is injected into the LC/ MS system and the cations, [M + H] +, of each compound monitored at pH 2.0; the anions, [M – H] –, and the cations, [M + H]+, of each component are simultaneously monitored at pH 7.4 and 10.5. The same approach is recommended for CHI determination of each component from mixtures of different compounds. © 2012 Taylor & Francis Group, LLC

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This LC/MS method was tested for a number of commercial products analyzed after preparation of suitable mixtures and data obtained were compared with those obtained from the original LC/UV approach. The comparison between the CHI values obtained from the two methods for a set of 32 drug-like compounds is reported in Table 8.2 showing an excellent agreement between the two sets of measurements.

Table 8.2 CHI Values for Compounds of Validation Mixture Determined by LC/MS and LC/UV Compound

CAS

pH 2.0

Δ

59-66-5 315-30-0 73-48-3 94-09-7 91-33-8 378-44-9 94-25-7 94-26-8 298-46-4 78-44-4 50-63-5 88-04-0 94-20-2 2030-63-9 548-73-2 25812-30-0 50-23-7 135-09-1 606-17-7 59-87-0 129-20-4 63-98-9 50-33-9 53-03-2 125-33-7 94-24-6 60-54-8 738-70-5 522-66-7 480-16-0 118-55-8 57-83-0

23.22 23.02 0.20 11.54 11.54 0.00 –48.05 7.49 7.23 0.26 –14.55 –14.55 0.00 –43.62 72.90 72.88 0.01 75.86 75.86 0.00 67.42 58.82 58.76 0.07 63.26 63.26 0.00 64.09 67.52 67.48 0.03 56.52 56.52 0.00 44.32 59.65 59.59 0.06 59.21 59.21 0.00 60.46 82.42 82.44 –0.02 80.80 80.80 0.00 81.44 82.42 82.44 –0.02 79.90 79.90 0.00 47.55 60.48 60.42 0.06 61.46 61.46 0.00 64.09 67.52 67.48 0.03 28.63 28.63 0.00 67.32 14.53 14.29 0.23 84.40 84.40 0.00 58.44 82.42 82.44 –0.02 79.90 79.90 0.00 77.00 69.17 69.14 0.03 32.68 32.68 0.00 35.45 61.31 61.25 0.06 124.88 124.88 0.00 158.89 36.47 36.32 0.15 76.75 76.75 0.00 77.81 101.05 101.14 –0.09 65.51 65.51 0.00 51.18 52.61 52.52 0.09 52.02 52.02 0.00 53.60 42.68 42.55 0.13 44.82 44.82 0.00 93.14 83.66 83.69 –0.03 26.38 26.38 0.00 28.59 34.81 34.65 0.16 37.18 37.18 0.00 40.69 65.45 65.40 0.04 34.48 34.48 0.00 27.79 44.33 44.21 0.12 43.92 43.92 0.00 48.36 94.84 94.91 –0.07 46.17 46.17 0.00 43.11 53.44 53.35 0.09 53.82 53.82 0.00 55.22 37.30 37.15 0.15 36.28 36.28 0.00 39.89 39.37 39.23 0.14 84.40 84.40 0.00 84.66 55.10 55.02 0.08 48.87 48.87 0.00 51.18 20.74 20.53 0.21 42.12 42.12 0.00 45.13 17.84 17.62 0.22 67.31 67.31 0.00 72.56 50.54 50.44 0.10 30.43 30.43 0.00 –45.63 101.05 101.14 –0.09 99.08 99.15 0.07 99.51 100.22 100.31 –0.09 96.09 96.09 0.00 93.14

–48.05 –43.62 67.38 64.09 44.32 60.46 81.44 47.55 64.09 67.32 58.44 77.00 35.45 158.89 77.81 51.18 53.60 93.12 28.59 40.69 27.78 48.36 43.11 55.22 39.89 84.66 51.18 45.13 72.56 –45.63 99.59 93.14

0.00 0.00 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.08 0.00

CHI

UV

Δ

pH 10.5 CHIUV

CHI Acetazolamide Allopurinol Bendroflumethiazide Benzocaine Benzthiazide Betamethasone Butamben Butylparaben Carbamazepine Carisoprodol Chloroquine Chloroxylenol Chlorpropamide Clofazimine Droperidol Gemfibrozil (waxy) Hydrocortisone Hydroflumethiazide Iodipamide Nitrofurazone Oxyphenbutazone Phenacemide Phenylbutazone Prednisone Primidone Tetracaine Tetracycline Trimethoprim Hydroquinine Morin hydrate Phenyl salicylate Progesterone

pH 7.4

MS

MS

CHI

MS

CHI

UV

Δ

CHI

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Samples

HPLC system

Column

UV detector Time

(a) Injection

Samples in mixture

HPLC system

Mass 1 Column

MS detector

Mass 2 Mass 3

(b)

Time

Figure 8.3  General setup of CHI determination method: (a) LC/UV; (b) LC/MS. (From Camurri, G. and Zaramella, A., 2001, Analytical Chemistry 73:3716–3722.)

However, the comparison of results obtained from another set of DNA GyraseB inhibitors, the molecular formulae of which were not given, showed divergences in the range of 0–3 CHI units. These differences are compatible with the experimental error of the method. It should be pointed out that the use of mass spectrometry detection does not require full chromatographic separation of each compound prior to its identification and the subsequent determination of its CHI. This basic difference between the two methods shows two advantages: first, a significant number of compounds, up to 32 compounds in the Camurri and Zaramella instrument [23], can be injected simultaneously into the LC/MS system, reducing the analysis time significantly and, second, compounds without chromophores that are not suitable for LC/UV detection can be analyzed by means of the LC/MS method. Figure 8.3 allows an easy comparison of the original and LC/MS procedures.

8.2  Linear Solvation Energy Relationships and Comparison to Other Lipophilicity Scales 8.2.1  Linear Solvation Energy Relationships Most chromatographic parameters, such as CHI, are related to the distribution constant of the solute between the mobile and stationary phases, which in turn can be related to the free energy needed to transfer the solute between both phases. This free energy is the difference between the solvation energy of the solute in mobile and stationary phases.

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It is commonly accepted that the free energy of a process can be obtained by an additive combination of the free energies of the different chemical interactions that contribute to the overall process, each one proportional to a product of appropriate descriptors of the different compounds that interact. Thus, any free-energy related parameter can be described with a linear combination of these products (linear-free energy relationships [LFERs]). Linear solvation energy relationships (LSERs) are particular cases of LFERs for solvation processes, such as liquid chromatography distribution. One of the most successful LSER approaches is the solvation parameter model developed by Abraham [24]. Since the solute property correlated to the solvation descriptors can be any property related to free energy, the solvation parameter model has been successfully applied to characterize many physicochemical and biological processes, such as solvent–water partition processes (including octanol–water partitions) [25–27], reversed-phase liquid chromatography systems [28–33], electrokinetic separation systems [34], drug transport across the blood–brain barrier [35–37], human intestinal absorption [38], skin permeation and partition [39], tadpole narcosis [40], chemical toxicity for several aquatic organisms [41,42], and soil–water sorption [43]. The Abraham solvation parameter model is based on the following equation:

log SP = c + eE + sS + aA + bB + vV

(8.5)

where SP is the dependent solute property in a given system and can be an equilibrium constant or some other free energy related property. The E, S, A, B, and V independent variables are the solute descriptors proposed by Abraham. E represents the excess molar refraction; S the solute dipolarity/polarizability; A and B the solute’s effective hydrogen-bond acidity and hydrogen-bond basicity, respectively; and V McGowan’s solute volume. The coefficients of the equation are characteristic of the system and reflect its complementary properties to the corresponding solute property. As they represent the difference in solvation properties between the two phases that compose the system, e refers to the difference in capacity of each phase to interact with solute π- and n-electrons; s is a measure of the difference of the two phases in capacity to take part in dipole–dipole and dipole-induced dipole interactions; a and b represent the differences in hydrogen-bond basicity and acidity, respectively, between both phases; and v is a measure of the relative ease of forming a cavity for the solute in the two phases. For any system, the coefficients of the correlation equation can be obtained by multiple linear regression analysis between the log SP values acquired for an appropriate group of solutes and their descriptor values. The solvation parameter model has been widely applied to reversed-phase liquid chromatography systems [28–32,44]. Commonly, the SP property is the retention factor (k) of a series of solutes in a particular isocratic HPLC system (fixed column and mobile phase). Although the CHI descriptor is a parameter linearly related to gradient retention times, rather than to isocratic retention factors, linear relationships between both types © 2012 Taylor & Francis Group, LLC

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Table 8.3 System Constants and Statistics of the Application of Equation 8.5 to the CHI Descriptor of 29 Compounds in a Variety of HPLC Columns with Acetonitrile–Water Mobile Phase Column ODS2-IK5 Inertsil Symmetry C18 NovaPak RP Supelcosil ABZ Selectosil RP Prodigy ODS2 Spherisorb ODS1 Unisphere C18 Unisphere PBD Asahipak ODP RPS40 Novapak Phenyl Novapak-CN Diol-YC5 Inertsil Selectosil-diol RexChrom IAM PC2 Nucleosil NH2 Nucleodex b PM

c

e

s

a

b

v

R

SD

28.6 44.6 41.9 35.6 43.2 39.8 37.5 35.7 35.4 52.2 60.6 43.1 –18.0 –22.8 –41.3 0.7 –40.5 36.5

5.9 3.4 3.4 6.5 4.0 3.4 4.0 12.8 11.8 6.3 10.0 1.8 9.0 16.5 27.0 10.2 15.1 7.5

–15.3 –10.8 –12.2 –10.9 –10.1 –12.4 –7.5 –12.1 –10.4 –3.2 –3.9 –3.1 –13.1 –23.0 –29.4 –11.0 –17.4 –4.2

–19.2 –22.5 –22.6 –13.4 –25.1 –23.2 –25.0 –16.7 –18.4 –23.4 –36.1 –26.9 –7.1 –12.1 –4.3 6.5 3.7 –1.9

–63.7 –60.3 –57.4 –68.1 –62.0 –61.9 –56.4 –72.6 –74.7 –78.5 –64.7 –63.0 –30.0 –28.9 –39.3 –47.4 –35.4 –52.0

65.0 56.2 57.8 63.5 57.2 58.1 57.7 63.0 63.7 51.2 39.4 54.1 48.8 50.0 61.6 44.0 57.1 31.5

0.987 0.990 0.993 0.974 0.995 0.993 0.982 0.981 0.969 0.980 0.990 0.981 0.957 0.930 0.903 0.972 0.939 0.970

4.5 3.4 3.0 5.5 2.3 3.0 4.6 4.9 6.6 5.0 3.4 4.5 5.3 7.7 10.7 3.4 7.9 4.9

of parameters have been demonstrated [45]. Thus, the solvation parameter model should be also directly applicable to CHI [46]. Table 8.3 reports the results obtained for the CHI value of 29 compounds determined in a variety of HPLC systems with different columns. In all cases, good statistically significant correlations were found. The coefficients obtained reflect the effect and importance of the solute properties in the CHI parameter. s, a (except for amino and IAM), and b are negative, showing that an increase in solute polarity, hydrogen bond acidity, and hydrogen-bond basicity decreases the hydrophobicity (CHI value) of the compound. e and v are positive, which indicates that an increase in solute polarizability or volume increases hydrophobicity (CHI value). The properties primarily affecting hydrophobicity are solute hydrogenbond basicity and volume, which have the largest coefficients (b and v) in absolute value.

8.2.2  Comparison to Isocratic HPLC Retention The results of Table 8.3 are similar to those obtained for isocratic HPLC retention [29,30,44]. In order to compare various partition systems, it is useful to set out the normalized coefficients [29] or the coefficient ratios [30,40]. The coefficient ratios (referred to as v) for several selected columns of Table 8.3 are presented in Table 8.4, together with those of other HPLC systems. © 2012 Taylor & Francis Group, LLC

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Stationary Phase

C18 C18 C18 C18 C18 C18 Polymeric Polymeric Polymeric IAM IAM IAM IAM Phenyl Cyano Diol Amino Cyclodextrine

Parameter

CHIODS CHIODS CHIODS log k log k log k CHIPOL log k log k CHIIAM log k log k log k CHIPHEN CHINCN CHIDIOL CHINH2 CHICD

ODS2-IK5 Inertsil Symmetry C18 Supelcosil ABZ Average 9 ODS columns XTerra MSC18 XTerra RP18 RPS40 PRP-1 PRP-1 RexChrom IAM PC2 DPC coated Regis IAM.PC.MG Regis IAM.PC.DD2 Novapak Phenyl Novapak-CN Diol-YC5 Inertsil Nucleosil NH2 Nucleodex b PM

Column 0%–100% ACN gradient 0%–100% ACN gradient 0%–100% ACN gradient 20%–90% ACN isocratic 40% ACN 40% ACN 0%–100% ACN gradient 100% ACN 67% ACN 0%–100% ACN gradient 10% ACN 10% ACN 40% ACN 0%–100% ACN gradient 0%–100% ACN gradient 0%–100% ACN gradient 0%–100% ACN gradient 0%–100% ACN gradient

Mobile Phase 0.09 0.06 0.10 0.18 0.09 0.15 0.25 1.15 0.28 0.23 0.18 0.43 0.25 0.03 0.18 0.33 0.27 0.24

e/v –0.24 –0.19 –0.17 –0.33 –0.26 –0.29 –0.01 –0.66 –0.10 –0.25 –0.16 –0.23 –0.30 –0.05 –0.27 –0.46 –0.30 0.13

s/v –0.30 –0.40 –0.21 –0.26 –0.24 –0.16 –0.92 –1.19 –0.76 0.15 0.01 0.37 0.12 –0.50 –0.15 –0.24 0.07 –0.06

a/v –0.98 –1.07 –1.09 –0.92 –0.98 –0.99 –1.64 –1.75 –1.45 –1.08 –1.03 –1.07 –1.03 –1.17 –0.61 –0.58 –0.62 –1.65

b/v

46 46 46 30 29 29 46 44 44 46 44, 47 44 29 46 46 46 46 46

Ref.

Table 8.4 Ratios of the Regression Coefficients of Equation 8.5 for Some CHI Systems Selected from Table 8.3 and for Some Comparable HPLC log k Systems Selected from the Literature

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389

The coefficient ratios for the CHI determined in C18 columns are remarkably similar to those obtained for the isocratic log k values in a variety of ODS columns with different quality of the silica support in several methanol–water and acetonitrile–water mobile phases. Coefficient ratios for the polymer-based column (CHIPOL) are very different from those for all the other columns, with large negative a/v and b/v ratios. There are correlation data for only one polymeric column (PRP-1) [44]. Although it is not expected that the two different polymer columns behave in exactly the same way, it is interesting that the PRP-1 column also gives large negative a/v and b/v ratios. The only other column that can be compared is the immobilized artificial membrane (IAM) column. CHIIAM coefficient ratios are remarkably close to those obtained by Miyake and co-workers for a self-made IAM coated column and 10%–30% of acetonitrile [47]; Abraham and co-workers for IAM.PC.MG column and 0%–35% acetonitrile [44]; and Lázaro and co-workers for IAM column and 10%–60% acetonitrile [29]. Details in Table 8.4 are presented for 10% acetonitrile in the Miyake and Abraham columns and 40% acetonitrile in the Lázaro column. These results strongly suggest that the factors that influence isocratic retention are the same as those that influence CHI determination by the fast gradient elution. That is, the same information can be obtained more quickly with the CHI descriptor [46]. Because there is a good linear correlation between log kIAM values and CHIIAM values, the latter can be used to characterize the interactions of drugs with IAM. This method provides a fast and easily automated screen for modeling the membrane interaction of a large number of new molecular entities [48]. Table 8.4 also points out that the information carried out by the CHI descriptor is different for each column type, although for each type of column it is poorly sensitive to variations in silica support and makers. This last point was also tested by a principal component analysis of the CHI descriptor values of the 29 studied compounds in the different columns of Table 8.3 [46]. The first principal component explained 89% of the total variance, indicating a high degree of similarity for the retention mechanisms that operate in all columns. The nonlinear map of the column component loadings is presented in Figure 8.4 for the first four principal components. It can be seen that the points representing ODS columns are very close to each other. The aminopropyl, diol, and nitrile columns represent different selectivity and lie above the ODS type columns. Cyclodextrin- and polymer-based columns are on the opposite end. The IAM column represents another type of selectivity on the right-hand side of the plot.

8.2.3  Comparison to Other Hydrophobicity Parameters The coefficient ratios in Table  8.4 can be also used to test the similarity of the CHI with other hydrophobicity parameters, such as partition coefficients (log P). Table 8.5 presents the coefficient ratios for other distribution systems, such as octanol–water, hexane–water, blood–brain barrier, etc. There are very large variations in coefficient ratios of the systems, and thus it is important to specify the water–organic solvent system used to measure hydrophobicity [25,49]. If, as usual, the water–octanol system (log Po/w) is chosen as the standard system for hydrophobicity, then the © 2012 Taylor & Francis Group, LLC

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200

CHI indiol

150

CHI sdiol

CHI ON

CHI OD1

100

CHIIAM CHI pol

50

0

CHI NH2

0

50

CHI apo

100

150 (a)

180

CHI OD

200

250

300

CHI CO1

160 140 120

CHI in MeOH

100

CHI In

CHI SRP CHI in ph

CHI Prod

80 60

CHI NRP CHI Sy

CHI ABZ

CH BRP

40 20 0

0

50

100

150 (b)

200

250

300

Figure 8.4  Map of column principal component loadings (the first four principal components were taken into account). (a) All columns; (b) only the nonpolar columns. (From Valkó, K. et al., 1998, Journal of Chromatography A 797:41–55.)

coefficients’ ratios of this system have to be compared with those of the CHI systems of Table 8.4. It can be observed that the coefficients’ ratios for CHI in ODS columns (indicated as CHIODS) are quite similar, except for the a/v ratio, which is negative for CHIODS and almost zero for the octanol–water partition. Thus, using CHIODS to compute log Po/w will not be good for solutes that are hydrogen-bond acids. However, the coefficient ratios for CHIIAM are also quite similar to those of octanol–water partition. Even the a/v ratio is closer to that of octanol–water (0.01) for CHIIAM (0.15) than for CHIODS (around –0.3). Thus, in principle, CHIIAM should provide a better correspondence to log Po/w than CHIODS. This was investigated in a further study [48], where CHI values for 48 compounds were determined in an IAM © 2012 Taylor & Francis Group, LLC

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Chromatographic Hydrophobicity Index (CHI)

Table 8.5 Coefficient Ratios in the Solvation Equations for Several Distribution Systems System

e/v

s/v

a/v

b/v

Octanol–water Isobutanol–water Pentanol–water Alkane–water Cyclohexane–water Hexadecane–water Blood–brain barrier

0.15 0.17 0.18 0.15 0.18 0.15 0.19

–0.28 –0.23 –0.24 –0.39 –0.37 –0.36 –0.69

0.01 –0.02 0.00 –0.82 0.81 –0.81 –0.72

–0.91 –0.83 –0.87 –1.13 –1.06 –1.10 –1.28

column in a mobile phase with 20% acetonitrile. The CHI values were measured at different pH values and combined to get a set of CHI descriptors for the neutral forms of the compounds. The CHI values were correlated with solute descriptors through Equation (8.5) and the coefficient ratios compared to those of isocratic log k at 20% acetonitrile, log k extrapolated to 0% acetonitrile (log k w), log Po/w, and CHIODS. The results are presented in Table 8.6. Table  8.6 shows that the relative coefficients of the solvation equations for the isocratic (log k) and gradient IAM (CHIIAM) are very similar. They are also similar to those of log Po/w. In fact, we can see that the CHIIAM lipophilicity scale is much closer to the octanol–water lipophilicity scale than the CHIODS lipophilicity scale. The correlation between the log Po/w and CHIIAM lipophilicity scales can be also observed in Figure 8.5 for the studied compounds in neutral form. This correlation can be described by means of the following equation: log Po/w = 0.473 + 0.0608 CHIIAM



(8.6)

n = 46, R2 = 0.83, with two outliers: salicylic and 4-nitrobenzoic acids. Table 8.6 Relative Regression Coefficients and Statistical Parameters of Solvation Equations Obtained for Isocratic and Gradient Retention Data on IAM Column with Acetonitrile, log Po/w , and CHI Values on an Intersil ODS Column with Acetonitrile Solute property

e/v

s/v

a/v

b/v

N

R

SD

log kIAM (20%) log kIAM extrapol. to 0 CHIIAM (neutral) log Po/w CHIODS

0.04 0.11 0.15 0.13 0.16

–0.11 –0.03 –0.17 –0.26 –0.24

0.12 0.12 0.14 0.02 –0.29

–1.07 –1.04 –1.04 –0.93 –1.01

44 44 46 46 44

0.971 0.964 0.969 0.997 0.985

0.17 0.27 4.67 0.10 5.07

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Martí Rosés, Elisabeth Bosch, Clara Ràfols, and Elisabet Fuguet y = 0.0608× + 0.4729 R2 = 0.8316

logP 6 5 4 3

Salicylic acid

2

4-nitrobenzoic acid

1 –30

–10

0 –0 –2

10

30

50

70

CHI (IAM, neutral)

Figure 8.5  Plot of log Po/w values and CHIIAM neutral. (From Valkó, K. et al., 2000, Journal of Pharmaceutical Sciences 89:1085–1096.)

The determination of log Po/w lipophilicity by the classical shake flask method is tedious and time consuming. The determination of log Po/w from CHI values is very fast (cycle time of 5–10 min) and offers the additional advantages of HPLC techniques for lipophilicity determination. Correlation in Equation (8.6) can be used to convert CHI IAM to log Po/w. However, IAM columns are less common and more delicate than ODS columns. Thus, determination of log Po/w from CHIODS was also attempted [50]. The main difference between log Po/w and CHIODS is the a/v ratio (see Table 8.6), which is almost zero for log Po/w and quite negative for CHIODS. This implies that an increase in the hydrogen bond acidity of the solute decreases CHIODS (and HPLC retention in C18 columns), whereas it practically does not affect octanol–water partition. This is because C18 columns are much less hydrogen-bond basic than acetonitrile–water mobile phases, whereas wet octanol has almost the same hydrogen bond basicity as water [51]. Thus, a correction term for solute hydrogen bond acidity is needed to get good relationships between HPLC retention parameters and octanol–water partition coefficients. In an interesting study, Valkó, Abraham, and co-workers [50] established the following relationships from a wide set of data:

log Po/w = 0.054CHIODS + 1.319A – 1.877

(8.7)

n = 86, R = 0.970, F = 655

log Po/w = 0.047CHIODS + 0.36HBC – 1.10

(8.8)

n = 86, R = 0.943, F = 336, where A is the Abraham solvation parameter for solute hydrogen bond acidity (see Equation 8.5) and HBC is simply a count of potential hydrogen bond acidic groups in the solute (in practice, number of –OH and –NH bonds). CHIODS must be measured in acetonitrile–water mobile phases because CHIODS in methanol–water phases differs from log Po/w not only in the hydrogen bond acidity © 2012 Taylor & Francis Group, LLC

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Chromatographic Hydrophobicity Index (CHI)

393

term (a/v) but also in the dipolarity/polarizability (s/v) and hydrogen bond basicity (b/v) terms. Therefore, to match the CHIODS in methanol scale with log Po/w scale, these three other terms should be also corrected. Equation (8.7) offers a simple way to determine the log Po/w of any neutral compound from the CHI value determined in any standardized common C18 column by the fast gradient method, provided that the hydrogen bond acidity A descriptor for the tested solute is known. For solutes with unknown A descriptors, Equation (8.8) can also provide slightly less precise but still reliable log Po/w values. Both equations were validated with test sets of reliable experimental log Po/w values for 40 drug molecules and calculated ClogPo/w values for 334 novel compounds [50]. The method has been also successfully tested with several series of compounds [52] including a family of steroids with log Po/w values between 1.61 and 4.94 (r 2 = 0.97) [53].

8.3  Determination of CHI for Ionizable Compounds 8.3.1  Relationship between CHI and pH Since many drug molecules have acid–base properties, the CHI parameter is usually measured at three different starting mobile phase pH values (pH = 2, pH = 7.4, and pH = 10.5; see Table 8.2), and the highest of the three CHI values obtained for the same compound is set as the hydrophobicity of the molecule. However, sometimes the neutral form of the different acid–base species cannot be achieved at these pH values, especially for very strong bases, very strong acids, or amphoteric compounds. To solve this problem, Canals et al. developed a fitting model to calculate the CHI lipophilicity of the different drug species from CHI data at different starting aqueous pH values [54]. When a gradient elution is performed, the concentration of organic solvent in the mobile phase continuously changes, as well as its pH and the pKa value of the compound being measured. The pH change of the mobile phase with increasing concentration of methanol and acetonitrile, using ammonium acetate buffers adjusted to different pH values as starting mobile phases, was measured. Since the variation of the mobile phase pH during gradient elution can be easily related to the measured pH value of the aqueous buffer before it is mixed with the organic solvent, if the same aqueous buffer is used in all the experiments [54–60], good relationships between gradient retention time and aqueous measured pH were obtained. An equation was proposed to describe the dependence of gradient retention times on the starting mobile phase pH for monoprotic neutral compounds [54]:

tg =

t gHA 10 s ( pK a − pH ) + t gA 10 s ( pK a − pH ) + 1

(8.9)

In this equation, tgHA and tgA are the gradient retention times of the acid (HA for neutral acids and HA+ for neutral bases) and basic (A– for neutral acids and A for neutral bases) forms of the compounds, respectively. pKa is the acid dissociation © 2012 Taylor & Francis Group, LLC

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constant and s is an empirical parameter added to correct the distortion in the pKa– pH term caused by the gradient. This model was successfully tested with some monoprotic model compounds (two acids and nine bases) with known pKa values in water [54]. As tg relates directly to CHI through the calibration equation (Equation 8.4), the combination of Equation (8.9) and Equation (8.4) provides the following expression that relates CHI with the aqueous pH of the mobile phase:

CHI =

CHI HA 10 s ( pK a − pH ) + CHI A 10 s ( pK a − pH ) + 1

(8.10)

As tg in Equation (8.9), CHIHA and CHIA correspond to the CHI values of the acidic and basic forms of the compounds, respectively. In order to obtain the CHI versus pH profile for a given compound, measurements of the CHI parameter at different starting pH values are needed. Although the calibration curves should be the same at all pH values because the compounds used for calibration are not affected by pH changes, different amounts of concentrated acid or base must be added to the aqueous buffers to reach the desired pH value while preparing the mobile phases. Therefore, although the buffer electrolyte concentration is always the same, the small variation from one buffer to the other can cause small differences in the retention time of the calibration set. In order to be more accurate in the calculations, it is advised to perform a calibration at all pH values instead of using one general calibration curve. In fact, Equation (8.10) is more precise than Equation (8.9) because calibration by Equation (8.4) at each pH value corrects for variation of buffer concentrations. Both Equations (8.9) and (8.10) were tested [61] for the same set of compounds, and it was concluded that the results of both approaches are comparable in terms of compound behavior, but the statistics (overall standard deviation, SD, and Fisher’s F parameter) are better for the fits of CHI (Equation 8.10). Thus, calibration at each different mobile phase is recommended when performing studies with ionizable compounds. The equation proposed for monoprotic acids and bases was generalized [62] to explain the variation of CHI with pH for any polyprotic acid–base compound. Ionization degree is related to the acidity constants and pH; thus, the CHI value for a polyprotic compound can be expressed as a function of the pKa values of each species and the pH of the mobile phase by the general expression i

n

CHI Hn Az + CHI =

∑10

j =1

i =1

n

1+



∑ s j ( pH − pK aj )

∑10

i

CHI Hn − i Az − i

∑ s j ( pH − pK aj )



(8.11)

j =1

i =1

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Chromatographic Hydrophobicity Index (CHI)

395

where n is the total number of ionizable groups z is the maximum positive charge (in the fully protonated species) Ka1,...Kai..., Kan are the successive dissociation constants sj again reflects the dynamics of the gradient elution In fact, there is a change between the initial composition of the mobile phase and the particular composition where compound elutes that implies a higher change of the mobile phase for large elution times. Therefore, the compound pKa and the buffer pH variations, which depend on the percentage of organic solvent, are more important for compounds with large retention times (i.e., larger CHI values). This causes a distortion on the CHI versus pH plots since points with higher CHI are shifted more than points with smaller CHI. The parameter s corrects this effect by stretching or enlarging the pH–pKa difference in Equation (8.11). In the case of polyprotic compounds, as each species has its own retention time and each one is affected in a different degree by the gradient, different sj parameters (s1, s2,…,sn), one for each pKa value, must be considered in the general equation. This general model allows the estimation of the hydrophobicity of all the possible species of a compound or the calculation of the average hydrophobicity (CHI) of the compound at any pH value. The goodness of the model was tested in different experimental conditions for different types of compounds [61–63]. To perform these kinds of studies, several HPLC mobile phases with different starting pH (from 2 to 12, ΔpH = 1) must be prepared. The pH of the aqueous buffer is usually adjusted by the addition of different amounts of formic acid or ammonia. The gradient retention time of the compounds is then measured in all the mobile phases and later converted to CHI values through the calibration equation. These CHI values are plotted against the starting pH value and data are fitted to Equations (8.10) or (8.11), depending on the characteristics of the compound being analyzed.

8.3.2  CHI versus pH Profiles for Monoprotic Neutral Compounds The CHI versus pH profile of a set of 11 basic drugs was determined by Espinosa et al. [63], using as organic modifier 2,2,2-trifluoroethanol. This solvent was chosen because of its unique selectivity, since it has a strong H-bond donor and poor H-bond acceptor abilities [50,64]. The authors used two different buffering agents to prepare the mobile phases: 50 mM ammonium acetate (in the pH range from 2.68 to 9.96, using concentrated formic acid or ammonia solutions to reach the desired pH value) and 50 mM butylamine solutions (in the pH range from 4.11 to 11.94, using concentrated formic acid to adjust the pH). Results are shown in Table 8.7 and Figure 8.6. The most significant remark is that the parameters obtained with the two buffer solutions are different. Only the pKa, CHIHA+, and CHIA values of lidocaine show a good agreement between ammonia and butylamine buffers. Parameters of nicotine, procaine, and terbutaline show only a fair agreement, and all other bases show a © 2012 Taylor & Francis Group, LLC

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Lidocaine Nicotine Procaine Pyrilamine Diphenhydramine 4-tert-Butylbenzylamine Alprenolol Propranolol Oxprenolol Metoprolol Terbutaline

Compound

137-58-6 54-11-5 59-46-1 91-84-9 58-73-1 39895-55-1 13655-52-2 525-66-6 6452-71-7 51384-51-1 23031-25-6

CAS CHIHA

5.6 ± 0.2 42 ± 3 6.5 ± 0.1 11 ± 3 8.8 ± 0.2 31.5 ± 0.6 17 ± 241 70 ± 1 12 ± 4 69 ± 1 13 ± 9 57 ± 2 15 ± 20 61 ± 1 19 ± 172 62 ± 3 14 ± 21 60 ± 1 9.9 ± 0.6 50.7 ± 0.4 8.9 ± 0.4 12.4 ± 0.2

pKa 99 ± 2 80 ± 3 81 ± 5 2160 ± 3E6 210 ± 250 309 ± 904 639 ± 6021 3805 ± 2E6 499 ± 5140 102 ± 12 24 ± 2

CHIA 0.6 ± 0.1 0.35 ± 0.05 0.44 ± 0.06 0.3 ± 0.2 0.27 ± 0.08 0.2 ± 0.1 0.3 ± 0.1 0.2 ± 0.1 0.3 ± 0.1 0.35 ± 0.05 0.5 ± 0.1

s

Ammonium Acetate Buffers

184 602 636 60 337 213 258 126 166 987 189

F pKa

2.91 5.5 ± 0.1 1.65 6.27 ± 0.06 0.93 7.77 ± 0.09 1.15 10.09 ± 0.08 0.89 8.9 ± 0.9 1.40 8.8 ± 0.2 0.99 9.6 ± 0.2 1.47 9.6 ± 0.1 1.01 9.8 ± 0.1 0.49 9.3 ± 0.2 0.39 9.92 ± 0.07

SD

CHIA

43 ± 5 101.4 ± 0.8 10 ± 2 91.9 ± 0.7 26 ± 1 69.6 ± 0.9 72.3 ± 0.3 95.0 ± 0.9 61 ± 10 118 ± 16 58 ± 2 102 ± 3 61.8 ± 0.8 98 ± 2 61.2 ± 0.6 100 ± 2 60.7 ± 0.6 92 ± 2 48.8 ± 0.9 84 ± 2 10.0 ± 0.3 30.0 ± 0.7

CHIHA

Butylamine Buffers

1.1 ± 0.2 0.9 ± 0.1 0.56 ± 0.06 0.63 ± 0.06 0.2 ± 0.1 0.31 ± 0.06 0.43 ± 0.06 0.48 ± 0.05 0.47 ± 0.06 0.38 ± 0.05 0.9 ± 0.1

s

245 754 630 682 145 332 417 555 462 427 480

F

2.20 1.64 1.31 0.58 1.85 1.47 1.15 1.03 0.94 1.06 0.68

SD 8.42 8.90 8.92 9.00 9.70 10.08 10.08 10.08 10.08 12.01

7.73

pKa,aq

Table 8.7 CHI Values for Monoprotic Neutral Bases in Ammonium Acetate and Butylamine Buffers Obtained through Equation 8.10

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397

Chromatographic Hydrophobicity Index (CHI) 100 90

0

2

4

8 10 12 14 w pH

6

CHI

90 80 70 60 50 40 30 20 10 0

CHI

CHI

110 100 90 80 70 60 50 40 30

70 2

0

4

6

w

2

4

6

8 10 12 14

70 60 0

2

4

4

100 90 CHI

90 80

8 10 12 14 w pH

0

2

4

8 10 12 14 w pH

Propanolol 40

80

30

4

6

8 10 12 14

w pH w

80 70

50

0

2

4

6

8 10 12 14

w pH w

Oxprenolol

CHI

CHI

6

w

w

90

2

60

50

6

70

0

4-t-Butylbenzylamine

100

Alprenolol

20

60

10

50 40

8 10 12 14 w pH

60 2

50

6

70

0

80

110

60

50

90

w

70

8 10 12 14

Pyrilamine

Diphenhydramine

CHI

80

6

w pH w

CHI

CHI CHI

90

4

100

Procaine

100

2

110

120 110 100 90 80 70 60

w pH w

110

0

Nicotine

CHI 0

60

8 10 12 14

w pH w

Lidocaine 90 80 70 60 50 40 30 20

80

0

2

4

6

8 10 12 14 w pH w

Metoprolol

0

0

2

4

6

8 10 12 14

w pH w

Terbutaline

Figure 8.6  Variation of CHI with the pH of 2,2,2-trifluoroethanol–water mobile phase: (o) ammonium acetate buffers; (·) butylammonium formate buffers. (From Espinosa, S. et al., 2002, Journal of Chromatography A 954:77–87.)

good agreement for the CHI values of the ionic form (CHIHA+), but CHIA and pKa from ammonium acetate buffer are clearly overestimated. The reason for these discrepancies is evident when looking at Figure 8.6. The plots of pyrilamine, diphenhydramine, 4-tert-butylbenzylamine, alprenolol, propranolol, oxprenolol, and metoprolol show an exponential trend because the protonated form © 2012 Taylor & Francis Group, LLC

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of these bases predominates in the pH range covered by ammonium acetate buffers. Thus, the extrapolation leads to large CHI values for the neutral forms and to high pKa values. This extrapolation produces a large uncertainty in the calculated CHIA and pKa values, which can be observed in the standard deviation of these parameters given in Table 8.7. Only lidocaine, which has a low pKa value, and, in a minor degree, nicotine and procaine, with intermediate pKa values, arrive at a condition where there is a predominance of the neutral form of the base. However, butylamine buffers cover a more basic pH range and all studied bases arrive close to the plateau, where there is a predominance of the neutral form in the CHI versus pH plot. Therefore, parameters estimated for the neutral forms of strong bases with butylamine as buffer are more reliable than those estimated from the less basic ammonium acetate buffer. It can be concluded that Equation (8.10) is a fitting equation that leads to accurate CHIHA+ and CHIA values, provided that the experimental retention data are taken in the appropriate pH range. Later, the validity of the model was enlarged to common HPLC systems [61], testing it for a wider range of compounds, including monoprotic acids and bases of different chemical natures. Experiments were carried out in methanol and acetonitrile, the two most common HPLC organic modifiers, using ammonium acetate solutions at different starting pH values as aqueous buffer. Results of this study are presented in Tables 8.8 (methanol) and 8.9 (acetonitrile) and Figures 8.7 (methanol) and 8.8 (acetonitrile). The fits demonstrate again that the model explains accurately the variation of CHI with pH in both solvents, since statistics of the fits are good in almost all cases. Good agreement is observed for the CHI values of the neutral form of the analytes, regardless of the solvent used for elution. Nevertheless, even when the agreement is quite good, a real match between CHIHA values in both solvents is not really expected, since the calibration compounds have different values for each solvent, especially in the lower and upper part of the calibration range. Paracetamol is a clear example since its CHIHA value goes from 40.29 in methanol to approximately half the value (20.48) in acetonitrile [61]. The ionic forms of the compounds, however, do not behave in the same way. With the only exception of 2,6-dichlorophenol, clear differences are depicted in Figures 8.7 and 8.8 for CHIA values, depending on the solvent. The reasons for these discrepancies are diverse. Some compounds do not reach the plateau for ionic form, a fact that leads to an extrapolation that is different for both solvents. Another reason is the extrapolation performed in the calibration plot. Many ionic forms of acids and bases have CHI values below the lowest calibration compound (paracetamol). For methanol, CHI extrapolation starts below 40 and for acetonitrile below 20. Many ionic species have CHIA far below these values (even negative), especially in acetonitrile, where higher differences between the neutral and the ionic forms are observed. For this reason, although CHI of the ionic species can explain quite well the behavior of monoprotic acids and bases in terms of CHI, they must be carefully treated and interpreted. At a first glance, Tables 8.8 and 8.9 show some fits with poorer statistics, such as the ones of 2-naphthol, phenobarbital, benzimidazole, p-toluidine, ephedrine, imipramine, and nortriptyline because of the lack of experimental points in the regions of very high or very low pH values. In gradient elution, the pH of the mobile phase and the pKa of the compounds change continuously, depending on the content of © 2012 Taylor & Francis Group, LLC

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2,6-Dichlorophenol 2-Naphthol 3,5-Dichlorophenol Benzoic acid Ethylparaben Phenobarbital Ibuprofen Vanillin Aniline Benzimidazole Dextromethorphan Ephedrine Imipramine Nortriptyline Pyridine p-Toluidine Trazodone

Compound

87-65-0 135-19-3 591-35-5 65-85-0 120-47-8 50-06-6 15687-27-1 121-33-5 62-53-3 51-17-2 125-71-3 299-42-3 50-49-7 72-69-5 110-86-1 106-49-0 19794-93-5

CAS

CHIA 17 ± 2 29 ± 193 62.1 ± 0.3 –28.8 ± 0.8 37.4 ± 0.5 –28 ± 34 77.6 ± 0.5 –31.0 ± 0.6 43 ± 1 55.5 ± 0.8 100 ± 2 74 ± 5 98.6 ± 0.7 100 ± 2 46 ± 2 63.1 ± 0.8 86.1 ± 0.2

CHIHA 76.3 ± 0.7 76.09 ± 0.05 85.05 ± 0.08 65 ± 1 72.96 ± 0.06 66 ± 1 90.1 ± 0.6 56.2 ± 0.3 –23 ± 3 3±4 70 ± 2 44 ± 1 77 ± 1 78 ± 3 –33 ± 4 17 ± 2 66.9 ± 0.3

0.64 ± 0.07 1.9 ± 0.6 0.99 ± 0.04 1.20 ± 0.08 0.86 ± 0.02 0.4 ± 0.1 0.6 ± 0.1 1.22 ± 0.04 1.6 ± 0.4 0.52 ± 0.08 0.37 ± 0.1 0.3 ± 0.1 0.5 ± 0.1 0.3 ± 0.1 3±5 0.7 ± 0.1 1.2 ± 0.1

s 8.80 ± 0.09 11 ± 2 9.74 ± 0.02 5.42 ± 0.03 10.04 ± 0.02 10.5 ± 0.8 5.5 ± 0.2 8.60 ± 0.02 4.3 ± 0.1 3.9 ± 0.2 6.6 ± 0.3 8.4 ± 0.5 5.6 ± 0.2 6.2 ± 0.4 4.8 ± 0.3 4.0 ± 0.1 4.67 ± 0.04

pKa 1.49 0.13 0.20 1.78 0.15 2.60 0.71 0.74 3.63 1.66 2.06 1.84 1.21 1.78 5.73 1.85 0.42

SD 699 2,140 4,665 1,881 15,011 176 155 7,881 195 349 96 88 173 62 128 278 1,264

F 6.79 9.54 8.18 4.20 8.34 7.74 4.54 7.40 4.58 5.50 9.74 9.64 9.45 10.14 5.29 5.33 6.93

pKa,aq.

2.01 1.87 1.56 1.22 1.70 2.72 0.98 1.20 –0.24 –1.61 –3.09 –1.26 –3.85 –3.98 –0.46 –1.32 –2.26

ΔpKa

Table 8.8 CHI Values for Monoprotic Neutral Acids and Bases in a Methanol Mobile Phase Obtained through Equation 8.10

Chromatographic Hydrophobicity Index (CHI) 399

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2,6-Dichlorophenol 2-Naphthol 3,5-Dichlorophenol Benzoic acid Ethylparaben Phenobarbital Ibuprofen Vanillin Aniline Benzimidazole Dextromethorphan Ephedrine Imipramine Nortriptyline Pyridine p-Toluidine Trazodone

Compound

87-65-0 135-19-3 591-35-5 65-85-0 120-47-8 50-06-6 15687-27-1 121-33-5 62-53-3 51-17-2 125-71-3 299-42-3 50-49-7 72-69-5 110-86-1 106-49-0 19794-93-5

CAS

CHIA 24 ± 1 57 ± 3 41.8 ± 0.8 –87 ± 2 25.2 ± 0.4 9.1 ± 0.9 49.7 ± 0.7 –107 ± 2 37 ± 1 35.2 ± 0.6 122 ± 4 50 ± 1 122 ± 4 125 ± 10 29 ± 1 57 ± 1 76.7 ± 0.6

CHIHA 73.5 ± 0.6 71.2 ± 0.1 82.1 ± 0.2 50 ± 2 63.2 ± 0.1 52.1 ± 0.4 93 ± 1 41.3 ± 0.9 –95 ± 2 –85 ± 9 54 ± 2 26.3 ± 0.6 60 ± 6 60 ± 10 –102 ± 2 –38 ± 7 50 ± 1

0.84 ± 0.08 4 ± 123 1.23 ± 0.08 1.0 ± 0.1 1.29 ± 0.05 0.93 ± 0.09 0.62 ± 0.06 1.19 ± 0.09 1.2 ± 0.1 0.49 ± 0.04 1.0 ± 0.2 1.0 ± 0.3 0.3 ± 0.1 0.3 ± 0.2 3±2 0.63 ± 0.08 1.0 ± 0.2

s 8.37 ± 0.06 10 ± 5 9.75 ± 0.03 5.71 ± 0.05 9.72 ± 0.02 8.94 ± 0.05 5.60 ± 0.08 8.91 ± 0.03 4.28 ± 0.04 2.8 ± 0.2 8.5 ± 0.1 9.0 ± 0.1 6.1 ± 0.4 6.6 ± 0.7 4.8 ± 0.1 3.4 ± 0.1 4.9 ± 0.1

pKa 1.22 0.36 0.60 3.56 0.36 0.90 1.18 2.22 2.93 1.17 4.46 1.33 4.66 7.13 2.98 2.41 1.44

SD 917 443 1689 985 4228 1096 774 2317 1121 1857 130 158 77 31 1273 467 195

F 6.79 9.54 8.18 4.20 8.34 7.74 4.54 7.40 4.58 5.50 9.74 9.64 9.45 10.14 5.29 5.33 6.93

pKa,aq.

1.58 0.61 1.57 1.51 1.38 1.20 1.06 1.51 –0.30 –2.66 –1.28 –0.63 –3.34 –3.57 –0.45 –1.91 –2.05

ΔpKa

Table 8.9 CHI Values for Monoprotic Neutral Acids and Bases in an Acetonitrile Mobile Phase Obtained through Equation 8.10

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401

Chromatographic Hydrophobicity Index (CHI)

40

–30

20

–50

0

30

20

80

10

12

Ibuprofen

95

85

10

80

5

75

0 12

0

2

6 pH

8

10

Benzimidazole

30 20

CHI

60

50

0

2

4

6 pH

8

10

0 12

Vanillin

40

20

–20

20

0

2

4

6 pH

8

10

–40

50

75 70

30

65

25

60

20

55

15

50

10

45

5

Dextromethorphan

60

30

100

95

25

90

20

85

15

80

10

75 70

4

6 pH

8

10

12

0

40

dCHL/dpH

0 12

Ephedrine

0

2

4

6

35

8

10

12

0

Pyridine

15

30

80

85

10

10

60

–10

40

5

80

5

–30

20

0

75

0

–50

CHI

100

90

0

2

4

6 pH

8

10

12

Trazodone

25

50

40

80

20

40

30

75

15

30

20

70

10

20

10

65

5

10

0

60

0

10

10

50

85

8

8

20

90

6 pH

6 pH

95

50

4

4

pH

Nortriptyline

60

2

2

70

p-Toluidine

0

0

25

12

CHI

CHI

2

60

70

CHI

12

CHI

0

dCHL/dpH

10

10 0

100

0 12

70

10

Aniline

40

20

8

12

0

80

6 pH

10

–20

20

4

8

60

20

2

6 pH

0

30

0

4

60

30

Imipramine

2

20

30

100

0

80 70 60 50 40 30 20 10 0

80

90

12

Phenobarbital

20

40

10

0

80

40

8

12

40

40

6 pH

10

40

100

4

8

100

50

2

6 pH

60

50

0

4

60

110

0

2

120

60

10

CHI

10

–40

dCHL/dpH

60

CHI

4

dCHL/dpH

15

dCHL/dpH

CHI

90

40

40

CHI

8

70 60 50 40 30 20 10 0 –10

50

70

5 0

dCHL/dpH

–10

60

dCHL/dpH

60

6 pH

12

10

dCHL/dpH

80

10

4

10

8

15

70

0

2

4

6 pH

8

120

0

2

4

6 pH

8

10

12

dCHL/dpH

100

30

dCHL/dpH

50 CHI

120

2

6 pH

Ethylparaben

80

70

0

4

dCHL/dpH

CHI

140

2

20

75

CHI

Benzoic acid

90

0

dCHL/dpH

12

25

80

CHI

10

dCHL/dpH

8

30

85

CHI

6 pH

90

65

dCHL/dpH

4

3,5-Dichlorophenol 40 35 30 25 20 15 10 5 0

dCHL/dpH CHI

2

80 75 70 65 60 55 50 45 40

0

30

10

12

dCHL/dpH

0

2-Naphthol 90 80 70 60 50 40 30 20 10 0

dCHL/dpH

CHI

2,6-Dichlorophenol 90 80 70 60 50 40 30 20 10 0

Figure 8.7  CHI versus pH curves in methanol and its first derivative. (From Fuguet, E. et al., 2007, Journal of Chromatography A 1173:110–119.)

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organic solvent. This fact may induce a shift to higher or lower pH values in the retention time versus aqueous pH curves of the different compounds. When this shift is too large, it is not possible to fit the equation properly because the inflection point area is not well defined by experimental points, and then some of the parameters are overestimated in the fit. In this case, curves for 2-naphtol and phenobarbital are shifted to higher pH values in methanol (Figure  8.7), close to the high limit of the pH range studied, so that the plateau corresponding to the deprotonated form of the compounds is not well defined. Curves for benzimidazole and p-toluidine are shifted to low pH values in acetonitrile (Figure 8.8), close to the low pH limit of the range studied, and therefore the shape of the plot is not defined for the acidic form of the compounds. This fact justifies the high uncertainties of the parameters of these fits in Tables 8.8 and 8.9 since extrapolation leads to lower CHI and pKa values than the real ones for the acids and larger values for the bases. Some compounds show poorer statistics than others, especially dextrometh­ orphan, ephedrine, imipramine, and nortriptyline in methanol (Table 8.8). In these cases, the high uncertainties associated to the parameters and also to the statistics of the general fit to Equation (8.10) are caused by the small change of retention time between the neutral and the ionized forms of the compounds and, consequently, the mild CHI variation along the pH values when going from one species to the other. This makes the curves less defined, as can be seen in Figure  8.7. This fact is reflected in the low value of the s parameter since this parameter indicates the sharpness in going from the acidic to the basic form of the compound. The first derivative of CHI versus pH curve can be used to evaluate the magnitude of s parameter [54]. Figures  8.7 and 8.8 show the CHI versus pH curves together with the first derivatives in methanol and acetonitrile, respectively, for the studied compounds. Compounds with a high value of s parameter show a sharp change when going from one species to the other, and hence the first derivative offers a very narrow peak, as in pyridine. On the other hand, low s values imply a wider peak in the first derivative. In the case of the previously mentioned compounds, it is clearly observed how the first derivative is almost a flat line, and s values are the lowest ones, around 0.4 units. These compounds have in common that all of them change from the protonated to the deprotonated species around pH = 7. In fact, ammonium acetate provides two buffering systems (acetic acid–acetate and ammonia–ammonium ion) that cover more or less all the working pH range. Nevertheless, the area around pH 7 is localized in the limit between the two buffering systems, so probably this medium is poorly buffered. This fact would explain the poorer fit of the experimental points to the model for these compounds. pKa values estimated through Equation (8.10) cannot be directly compared to the aqueous pKa values presented also in Tables 8.8 and 8.9 because they have been obtained in methanol–water and acetonitrile–water mobile phases. The obtained pKa values would agree with the aqueous value only when the variation of the pKa of the compound during gradient elution matches exactly the buffer pH variation (i.e., pKa–pH in Equation 8.10 is constant with solvent change). © 2012 Taylor & Francis Group, LLC

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Ibuprofen

10

50

20

50

5

40

10

45

0 12

30

Benzimidazole

40

20

30

10

0

80

–20

60

–40

40

–60

20 0

2

4

6 pH

8

10

Imipramine

130

CHI

120 110 100 90 80 70 60 50

0

2

4

6 pH

8

10

p-Toluidine

10

–80

40 0

2

4

6 pH

8

10

200

–40

80 40

–80

0 12

Dextromethorphan

–120

0

2

4

6 pH

8

10

0 12

Ephedrine

100

55

110

80

50

30

90

60

45

25

40

20

70

40

35

15

50

20

30

10

130

130 120 110 100 90 80 70 60 50

0

2

4

6 pH

8

10

0 12

2

4

6 pH

20

8

10

12

Trazodone

80 70 60 50 40 30 20 10 0

4

6

8

10

12

0

Pyridine

25

65

20

–10

40

60

15

–30

20

55

10

200

30

150

–10

120

–50

80

–90

40

–130

60

CHI

2

70

10

0

2

4

6 pH

8

10

12

0

35

5

50 45

5 0

pH

Nortriptyline

0

35

25

30

dCHL/dpH

dCHL/dpH

120

30

0 12

Aniline

0 12

160

70

10

10

0

80

8

8

100

30

6 pH

6 pH

0

75

4

4

40

80

2

2

160

100

0

0

40

120

–50

10

80

80

0

80 70 60 50 40 30 20 10 0 12

8

20

10 0

50 CHI

70

12

6 pH

dCHL/dpH CHI

–80

4

30

20

200

CHI

dCHL/dpH

100

CHI

20

2

60

30

0 12

–40

140 120

0

Vanillin

–120

40

CHI

40

CHI

60

Phenobarbital

0 12

50

20

10

10

40

30

8

8

30

70

6 pH

6 pH

50

60

4

4

50

40

2

2

40

80

0

0

60

80

0 12

10

60

20

10

8

50

50

40

6 pH

Ethylparaben

70

60

50

4

CHI

CHI

dCHL/dpH

160 140 120 100 80 60 40 20 0 12

2

dCHL/dpH

30

55

dCHL/dpH

60

dCHL/dpH

10

15

dCHL/dpH

8

40

60

90

100

CHI

6 pH

70

0

60

dCHL/dpH

4

20

CHI

2

50

65

dCHL/dpH

CHI

0

80

CHI

Benzoic acid

60 40 20 0 –20 –40 –60 –80 –100

25

dCHL/dpH

10

70

dCHL/dpH

8

90

CHI

6 pH

3,5-Dichlorophenol

30

dCHL/dpH

4

2-Naphthol

75

dCHL/dpH

2

0

80 70 60 50 40 30 20 10 0 12

CHI

2,6-Dichlorophenol

dCHL/dpH

80 70 60 50 40 30 20 10 0

dCHL/dpH

CHI

Chromatographic Hydrophobicity Index (CHI)

0

2

4

6 pH

8

10

0 12

Figure 8.8  CHI versus pH curves in acetonitrile and its first derivative. (From Fuguet, E. et al., 2007, Journal of Chromatography A 1173:110–119.)

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Obtained pKa values show two marked tendencies depending on the acid–base nature of the compounds. Compared to water as solvent, acids have a higher pKa value in the hydro-organic system, independently of the organic solvent used. Bases behave in the opposite way since in the hydro-organic systems their pKa values are lower than in water (except for very high concentrations of the organic solvent). This behavior depends basically on how the pH of the media and the pKa of the compound change when organic solvent is present. Two main factors have to be considered in order to explain the differences. The first one, the variation of the pKa of the compound, depends on the nature of the substances. Dissociation of neutral acids is governed by electrostatic and specific solute–solvent interactions (solvation effects). In the dissociation of neutral or anionic acids, charges are created (HA ⇄ H+ + A–) and the dissociation process is disturbed when the dielectric constant of the medium decreases due to the increase in organic solvent content. Therefore, the pKa values of acids increase when the methanol or acetonitrile content increases. On the other hand, in the dissociation of bases, there is no change in the number of charges (HAn+ ⇄ H+ + A(n–1)+), so the change of the dielectric constant of the medium does not affect the dissociation process. In this case, the dissociation depends only on the solvation of the different species by the solvents of the mixture. For cationic acids, the decrease of the pKa due to the solvation of the organic solvent–water mixture is not balanced by the change of dielectric constant, so the pKa decreases. Nevertheless, electrostatic and solvation effects depend also on solute properties (charge, volume, polarity, hydrogen bond abilities, etc.); therefore, the variation of the dissociation constant with solvent composition is different for each compound [57,65,66]. The second factor to consider is how the pH of the medium changes with the increase of organic solvent composition. This depends on the effect of methanol and acetonitrile in the acetic acid–acetate and ammonium–ammonia pairs. pH of acetic acid–acetate buffer will behave as the pKa of a neutral acid; therefore, the pKa and the pH given by this buffer in aqueous solution will increase with the content of organic solvent. On the other hand, the pH of the pair ammonium–ammonia will behave as the pKa of a cationic acid, decreasing the pKa and the pH of the medium when the methanol or acetonitrile content increases (at least up to 90% methanol or 60% acetonitrile [66]). The evaluation of these two factors explains in some way the magnitude of the differences observed between the aqueous pKa and the pKa obtained through Equation (8.10) for the studied compounds. Tables 8.8 and 8.9 show the differences observed between the estimated and the aqueous pKa values. Except for benzoic acid and ibuprofen, all acids have the shift from the neutral to the ionic forms in the area buffered by the pair ammonium–ammonia. This means that their pKa value will be higher than in water since they are neutral acids; in addition, the pH of the medium will decrease. The difference (pKa–pH) for these compounds will be, therefore, highly positive. Then the pKa estimated through Equation (8.10) should be higher than the aqueous one. Ibuprofen and benzoic acid are also neutral acids, so their pKa increases with the addition of methanol or acetonitrile in the medium. Nevertheless, the shift to the anionic species is in the acetic–acetate buffered area, so the pH of the medium © 2012 Taylor & Francis Group, LLC

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405

will increase as well during gradient elution, although less than the pKa of the acid. For instance, pKa of acetic acid—and thus pH of the buffer—increases in 0.77 units when going from water to 50% methanol, whereas pKa of benzoic acid increases in 1.04 units [67]. This fact implies a lower positive difference between the estimated and the aqueous pKa values. When differences in methanol are checked, it is observed that benzoic acid and ibuprofen show the lowest positive differences, whereas the rest of the acids show larger differences. pKa differences for vanillin could be considered a bit lower than the expected ones. In this case, another factor should be taken into account since this compound elutes very fast and, therefore, the variation of their pKa and the pH of the buffer are less than for the other compounds, which are more retained. Although not exactly equal, the results obtained for the acetonitrile–water gradient elution follow the same trends as for methanol–water. Aniline and pyridine have very low retention times, so the solvent composition change during elution is very small and the differences between pKa values are much lower than for other compounds. The rest of the bases follow the expected behavior. Dextromethorphan and ephedrine are the only ones that elute in the ammonium– ammonia buffered region. For these bases, a low negative difference with respect to aqueous pKa is expected since the pH of the medium increases whereas the pKa decreases. These lower differences, compared to other bases, are observed when results in acetonitrile are checked. The ones in methanol do not follow the same trend but rather, as explained before, the fits for these compounds are not as good as for other substances due to the low buffering capacity in the shift area. The rest of the bases, which have the shift in the acetic–acetate buffering region, show the largest negative differences between both pKa values. This is in concordance with the fact that their pKa decreases with an increase of methanol or acetonitrile percentage and the increase of the pH of the buffer.

8.3.3  CHI versus pH Profiles for Polyprotic Compounds The goodness of the general model (Equation 8.11) was tested for diprotic compounds by means of 12 substances of different natures (diprotic neutral bases, diprotic neutral acids, and amphiprotic compounds that were nonzwitterionic and zwitterionic) selected for this purpose [62]. Equation (8.12) can be easily derived for diprotic compounds from the general Equation (8.11): CHI =



CHI H2 A + 10 s1 ( pH − pK1 ) CHI HA + 10 ( s1 ( pH − pK1 )+ s2 ( pH − pK 2 )) CHI A 1 + 10 s1 ( pH − pK1 ) + 10( s1 ( pH − pK1 )+ s2 ( pH − pK 2 ))

(8.12)

In this equation, the subscript H2A refers to H2A, H2A+, or H2A2+; the subscript HA indicates HA–, HA, or HA+; and the subscript A refers to A2–, A–, or A, depending on whether the neutral compound is a neutral acid, a neutral amphiprotic compound, or a neutral base, respectively. Equation (8.12) allows the estimation of the hydrophobicity (CHI) of any species of a given diprotic compound, as well as the average hydrophobicity of the compound © 2012 Taylor & Francis Group, LLC

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at any pH value. A total of seven parameters are needed in this equation, since the only variables are CHI and pH. When the general equation was applied to monoprotic compounds, only four fitting parameters were needed. However, when the model is applied to polyprotic compounds, three more parameters are estimated for each additional acidic or basic group of the compound (CHIHiA, si, and pKai). Thus, it is necessary to increase the number of experimental points when the number of acidity constants increases, in order to define well the CHI versus pH curves. Four different types of solutes were analyzed, so different types of curves were obtained. Figure 8.9 shows the CHI versus pH curves together with the first derivative

10

45

5

35

0

0

2

4

6 pH

8

10

12

Norfloxacin

70

–50 0

2

4

6 pH

8

–75 0

2

4

50 –25

–30 –50

0

2

4

30

–20

20

–30

10

–40 6 pH

8

6 pH

8

10

12

–100

10 –10

4

–125

200

–10

40

2

12

10

0

0

10

125

50

0

6 8 pH

Phenylalanine

Salicylic acid

60

CHI

–25

30

–150 12

10

25

50

CHI

CHI 30

75

–40

–120

150 50

125

–80

250

50

10

0

dCHI/dpH

55

225 175

dCHI/dpH

15

CHI

65

dCHI/dpH

20

dCHI/dpH

CHI

75

2-Aminophenol

40

25

10

dCHI/dpH

Quetiapine

85

–50 12

Figure 8.9  CHI versus pH curves in acetonitrile and its first derivative for several polyprotic compounds. (From Fuguet, E. et al., 2009, Journal of Chromatography A 1216:7798–7805.). © 2012 Taylor & Francis Group, LLC

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407

(right axis) for a neutral base, a nonzwitterionic amphiprotic compound, two zwitterionic amphiprotic compounds, and a neutral acid, respectively. In case of quetiapine, a neutral diprotic base, it is observed that CHI increases when pH increases; that is, the lowest CHI values correspond to the double-charged species (H2A2+). The singlecharged (HA+) ones have slightly higher hydrophobicity and, finally, the neutral species (A) are the ones with higher CHI value. It is deduced that the number of charges of a given species is very important in defining the shapes of the curves. In general, the neutral species have CHI values between 0 and 100, which is the common scale of CHI parameter. However, due to short retention time, some ionic forms can reach negative values. This is because the CHI approach was initially proposed for neutral compounds [22], so the normalization performed in order to make the parameter values go between 0 and 100 did not take into account such strongly polar (charged) and almost unretained species. In the case of 2-aminophenol, a nonzwitterionic amphiprotic compound, the lowest CHI values correspond to the species that predominate at the lowest and the highest pH values. This is because the charged species are the ones present in these regions (H2A+ at low pH and A– at high pH), whereas in the central pH zone, the neutral form of the compound (HA), which has higher hydrophobicity, predominates. This is in accordance with other hydrophobicity indicators, such as the octanol–water distribution coefficient (log D o/w) that, in the case of amphiprotic compounds, has the higher value at a pH where the neutral form predominates [68]. A different trend is observed for the zwitterionic amphiprotic compounds norfloxacin and phenylalanine (Figure 8.9). The norfloxacin CHI profile is like the one of 2-aminophenol since the zwitterionic form, which is positively and negatively charged at the same time, is the one with highest CHI value (bell-shaped curves). However, phenylalanine shows an opposite behavior because the zwitterionic form is the one with lowest CHI value (U-shaped curve). A possible explanation for the different retention of the zwitterionic forms would be based on the geometry of the compounds. Norfloxacin is a large molecule with three aromatic rings, which confer an important hydrophobic component to the compound. Moreover, charges are quite separated; this causes a small dipole moment in the molecule. This small dipole moment favors the interactions of the compound with the organic phase, so retention of the zwitterionic form increases. On the other hand, phenylalanine is a small molecule (only one ring) with the two charges very close to each other; this involves a high dipole moment. This high polarity of phenylalanine compared to norfloxacin favors its partition in the aqueous phase rather than in the organic phase, which lowers retention of the zwitterionic form. The last model compound is salicylic acid, a diprotic neutral acid that shows the expected profile since the highest CHI values are located in the low pH region, where the neutral form (H2A) of the acids predominates. As long as pH increases, the concentration of the single-charged form (HA–) increases and thus the hydrophobicity decreases. Finally, at high pH values, the doubly charged species (A2–) predominate, and the lowest CHI values are observed. With regard to the s parameter, its value depends on the retention of the three different species, which is determined by the mobile phase composition variation © 2012 Taylor & Francis Group, LLC

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from the beginning of the gradient to compound elution. In the case of polyprotic compounds, each species has its own retention time and they are affected in different degrees by the gradient, so as many s parameters as acidity constants must be considered. Although the interpretation of the s parameter is complex, first derivatives can be used to evaluate its effect in the curves. Also, an accurate interpretation of the differences in pKa for these complex compounds is a difficult task. However, a general trend is observed because, similarly to monoprotic compounds, in most cases the pKa estimated under gradient conditions is higher than the aqueous pKa for acidic groups, whereas for basic groups the opposite behavior is followed. It can be concluded that the CHI method is a good alternative to other hydrophobicity approaches when hydrophobicity versus pH profiles are needed, since it is a very fast method. The general model allows the estimation of the hydrophobicity of all the possible species of a compound or the calculation of the average hydrophobicity (CHI) of the compound at any pH value, and it does not require specific instrumentation (only an HPLC system).

8.4  Applications in Biological Processes As a lipophilic parameter, the CHI values have been used in the studies of oral bioavailability and as a tool in method development. The oral bioavailability is largely dependent on lipophilicity and solubility. Compounds highly lipophilic and poorly soluble in aqueous media have low bioavailability. This is the case of substituted dibenzepinones, which show high potency in p38 enzyme assays, because their high lipophilicity and low solubility present low bioavailability. The p38 mitogenactivated protein is a promising target for the treatment of chronic inflammatory diseases such as rheumatoid arthritis. In order to improve the bioavailability of substituted dibenzepinones, Karcher et al. [69] tried to optimize their physicochemical properties by synthesizing azaanalogue dibenzepinones. The characterization of these new compounds had been done measuring the lipophilicity with the CHI parameter. The CHI parameter was measured with MeOH as organic modifier. They found that the aza-dibenzoheptanone series had lower lipophilicity, with CHIMeOH values ranging from 66 to 81, than the corresponding carbon analogues, whose CHIMeOH values ranged from 82 to 88. The CHI lipophilic parameter has been also used to study the effect of structural modification on cucurbitacins cytotoxicity [70]. Cucurbitacins are particularly known in folk medicine for their strong purgative, anti-inflammatory, and hepatoprotective activities. It was found that the strong biological activity of cucurbitacins was very close to their toxic dose, which renders them unlikely biological agents. On the other side, methylation of the enolic hydroxyl of cucurbitacin E enhanced the antitumor activity and lowered the toxicity on mice. Cucurbitacin skeletons only differentiate from steroids by the presence of C19 methyl group at position 9 instead of the usual position 10 for steroids. Consequently, the more lipophilic compounds can cross the lipid bilayer more easily than their polar homologues, leading to differentiation in their partition between the media and cells. Moreover, lipophilicity also plays a dominant role in ligand–receptor interactions. Bartalis and Halaweish [70] suggested that cytotoxicity of cucurbitacins involves © 2012 Taylor & Francis Group, LLC

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Chromatographic Hydrophobicity Index (CHI) y = –0.0308× + 3.53 r = 0.901

2 17 1

0

25

45

65 CHI ACN (a)

85

105

y = –0.0955× + 7.7677 r = 0.918

3

log IC50 (uM)

log IC50 (uM)

3

2 17 1

0

50

60

65 70 CHI MeOH (b)

75

80

Figure 8.10  Relationship between cucurbitacin toxicity on HepG2 cells and CHI measured in (a) acetonitrile or (b) methanol. (From Bartalis, J., and Halaweish, F. T., 2005, Journal of Chromatography B 818:159–166.)

hydrophobic interaction with the target molecule inside the cell, and analogues with higher lipophilicity may have strong interaction. In order to correlate the lipophilicity with the cytotoxicity of cucurbitacins, the CHI parameter was used. Figure  8.10 shows the relationship obtained by Bartalis and Halaweish [70] between cucurbitacin toxicity on HepG2 cells and CHI measurements in acetonitrile and methanol. These good correlations suggest that compounds lipophilicity increases in vitro cytotoxicity. They noticed an increase in cytotoxicity for the alkylated derivatives on HepG2 cells. Additionally, cytotoxicity increased proportionally with increasing alkyl chain at C2 hydroxyl. Although the CHIMeOH hydrophobicity scale presents better correlation than the CHIACN scale, the latter has a larger range than the CHIMeOH scale. Therefore, it should provide a highly sensitive measure allowing more discrimination among similar compounds. CHI IAM has been used to evaluate the strength of interaction of cationic amphiphilic drugs (CADs) with phospholipids. CADs have some common chemical features that confer on them an affinity for cellular lipids and then can alter the metabolism of cells, leading to phospholipidosis. Owing to their polarity and the presence of hydrophobic portion, these drugs can interact with lipid cell components and cause disorders in phospholipid storage and, as a consequence, an abnormal cellular lipid accumulation, which leads to adverse effects in different organs. The ability to predict phospholipidosis and related disorder could play an important role in the early phases of the safety evaluation of a new drug. Electron microscopy (EM) is considered the most reliable method for phospholipidosis diagnosis. Nevertheless, this is an expensive technique characterized by a low throughput and requires in vivo studies. Casartelli et al. [71] proposed an in vitro biological model, which consists of a human monocyte-derived cell line, U-937, and fluorescence staining with a high affinity for lipids. The drug-induced intracellular phospholipid accumulation is measured by using Nile red, a probe that stains both neutral and polar lipids. © 2012 Taylor & Francis Group, LLC

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The test was evaluated using different CADs that were known to cause phospholipidosis in vivo. The U-937 data were compared with the CHIIAM parameter, which measures the drug interaction with phospholipids. A good correlation was obtained (r = 0.95) and, in general, non-CADs gave low CHIIAM values, further confirming the important role played by physical–chemical features in the development of phospholipidosis.

8.5  Conclusion The CHI descriptor is a measure of lipophilicity that can be calculated from chromatographic retention in a fast and reproducible way. It can be obtained by a gradient elution mode with methanol or acetonitrile as organic modifiers in a variety of columns in less than 10 min, after an appropriate standardization of the chromatographic system. Different CHI scales have been proposed, depending on the stationary phase (ODS, IAM, polymeric, etc.) and cosolvent (methanol, acetonitrile) used, that show different sensitivities to the chemical interactions implied in the partition process. The most interesting are the CHI scales obtained with ACN and ODS (CHIODS) and IAM (CHIIAM) columns, which show good correlations with other lipophilicity descriptors, such as log Po/w, as well as with some biological parameters. As with most lipophilicity parameters, CHI is sensitive to the pH of the medium. To obtain the CHI value of the neutral compound, it has been proposed to measure it at three pH values for the aqueous chromatographic buffer employed (ammonium acetate at pH 2, 7.4, and 10.5) and take the highest CHI value. On the other hand, a model has been proposed to find the CHI values measured at different pH values and thus to obtain the CHI values of the different acid–base species. The latter method also allows obtaining the CHI versus pH profiles.

Acknowledgment We are indebted to Dr. Klara Valkó for her corrections and helpful comments after a careful revision of our preliminary manuscript.

References

1. Testa B., Crivori P., Reist M., Carrupt P. 2000. The influence of lipophilicity on the pharmacokinetic behavior of drugs: Concepts and examples. Perspectives on Drug Discovery 19:179–211. 2. Valkó K., Reynolds D. P. 2005. High-throughput physicochemical and in vitro ADMET screening: A role in pharmaceutical profiling. American Journal of Drug Delivery 3:83–100. 3. Sangster J. 1997. Octanol–water partition coefficients: Fundamentals and physical chemistry. In Wiley Series in Solution Chemistry, 2nd ed., ed. P. G. T. Fogg. John Wiley & Sons, Chichester, UK. 4. EPA product properties test guidelines, OPPTS 830.7550, partition coefficient (n-octanol/water), shake flask method. 1996. Report no.: EPA 712–C–96–038. United States Environmental Protection Agency.

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5. Avdeef A. 1992. pH metric log P. Part 1. Difference plots for determining ion-pair octanol–water partition coefficients of multiprotic substances. Quantitative Structure– Activity Relationships 11:510–517. 6. Takács-Novák K., Avdeef A. 1996. Interlaboratory study of log P determination by shake-flask and potentiometric methods. Journal of Pharmaceutical and Biomedical Analysis 14:1405–1413. 7. Makovskaya V., Dean J. R., Tomlinson W. R., Hitchen S. M., Comber M. 1995. Determination of octanol—water partition coefficients using gradient liquid chromatography. Analytica Chimica Acta 315:183–192. 8. Benhaim D., Grushka E. 2008. Effect of n-octanol in the mobile phase on lipophilicity determination by reversed-phase high-performance liquid chromatography on a modified silica column. Journal of Chromatography A 1209:111–119. 9. Benhaim D., Grushka E. 2010. Characterization of Ascentis RP-amide column: Lipophilicity measurement and linear solvation energy relationships. Journal of Chromatography A 1217:65–74. 10. Liu X., Tanaka H., Yamauchi A., Testa B., Chuman H. 2005. Determination of lipophilicity by reversed-phase high-performance liquid chromatography: Influence of 1-octanol in the mobile phase. Journal of Chromatography A 1091:51–59. 11. Lombardo F., Shalaeva M. Y., Tupper K. A., Gao F., Abraham M. H. 2000. ElogPoct: A tool for lipophilicity determination in drug discovery. Journal of Medicinal Chemistry 43:2922–2928. 12. Giaginis C., Theocharis S., Tsantili-Kakoulidou A. 2007. Octanol/water partitioning simulation by reversed-phase high performance liquid chromatography for structurally diverse acidic drugs: Effect of n-octanol as mobile phase additive. Journal of Chromatography A 1166:116–125. 13. Donovan S. F., Pescatore M. C. 2002. Method for measuring the logarithm of the octanol–water partition coefficient by using short octadecyl–poly(vinyl alcohol) high-performance liquid chromatography columns. Journal of Chromatography A 952:47–61. 14. Vallat P., Fan W., Tayar N. E., Carrupt P., Testa B. 1992. Solvatochromic analysis of the retention mechanism of two novel stationary phases used for measuring lipophilicity by RP-HPLC. Journal of Liquid Chromatography 15:2133. 15. Kaliszan R., Haber P., Baczek T., Siluk D., Valkó K. 2002. Lipophilicity and pKa estimates from gradient high-performance liquid chromatography. Journal of Chromatography A 965:117–127. 16. Wiczling P., Waszczuk-Jankowska M., Markuszewski M. J., Kaliszan R. 2008. The application of gradient reversed-phase high-performance liquid chromatography to the pKa and log kw determination of polyprotic analytes. Journal of Chromatography A 1214:109–114. 17. Tate P. A., Dorsey J. G. 2004. Column selection for liquid chromatographic estimation of the kw' hydrophobicity parameter. Journal of Chromatography A 1042:37–48. 18. Valkó K. 2004. Application of high-performance liquid chromatography based measurements of lipophilicity to model biological distribution. Journal of Chromatography A 1037:299–310. 19. Pallicer J. M., Pous-Torres S., Sales J., Rosés M., Ràfols C., Bosch E. 2010. Determination of the hydrophobicity of organic compounds measured as log Po/w through a new chromatographic method. Journal of Chromatography A 1217:3026–3037. 20. Valkó K., Slégel P. 1993. New chromatographic hydrophobicity index (φ0) based on the slope and the intercept of the log k' versus organic phase concentration plot. Journal of Chromatography A 631:49–61.

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21. Shoenmakers P. J., Billiet H. A. H., De Galan L. 1979. Influence of organic modifiers on the retention behavior in reversed-phase liquid chromatography and its consequences for gradient elution. Journal of Chromatography A 185:179–195. 22. Valkó K., Bevan C., Reynolds D. 1997. Chromatographic hydrophobicity index by fastgradient RP HPLC: A high-throughput alternative to log P/log D. Analytical Chemistry 69:2022–2029. 23. Camurri G., Zaramella A. 2001. High-throughput liquid chromatography/mass spectrometry method for the determination of the chromatographic hydrophobicity index. Analytical Chemistry 73:3716–3722. 24. Abraham M. H. 1993. Scales of solute hydrogen-bonding: Their construction and application to physicochemical and biochemical processes. Chemical Society Reviews 22:73–83. 25. Abraham M. H., Chadha H. S., Whiting G. S., Mitchell R. C. 1994. Hydrogen bonding. 32. An analysis of water–octanol and water–alkane partitioning and the delta log p parameter of seiler. Journal of Pharmaceutical Sciences 83:1085–1100. 26. Abraham M. H., Chadha H. S., Dixon J. P., Leo A. J. 1994. Hydrogen bonding. 39. The partition of solutes between water and various alcohols. Journal of Physical Organic Chemistry 7:712–716. 27. Abraham M. H., Zissimos A. M., Acree W. E. 2003. Partition of solutes into wet and dry ethers; an LFER analysis. New Journal of Chemistry 27:1041–1044. 28. Abraham M. H., Rosés M. 1994. Hydrogen bonding. 38. Effect of solute structure and mobile phase composition on reversed-phase high-performance liquid chromatographic capacity factors. Journal of Physical Organic Chemistry 7:672–684. 29. Lázaro E., Ràfols C., Abraham M. H., Rosés M. 2006. Chromatographic estimation of drug disposition properties by means of immobilized artificial membranes (IAM) and C18 columns. Journal of Medicinal Chemistry 49:4861–4870. 30. Abraham M. H., Rosés M., Poole C. F., Poole S. K. 1997. Hydrogen bonding. 42. Characterization of reversed-phase high-performance liquid chromatographic C18 stationary phases. Journal of Physical Organic Chemistry 10:358–368. 31. Bolliet D. F., Poole C., Rosés M. 1998. Conjoint prediction of the retention of neutral and ionic compounds (phenols) in reversed-phase liquid chromatography using the solvation parameter model. Analytica Chimica Acta 368:129–140. 32. Lepont C., Poole C. F. 2002. Retention characteristics of an immobilized artificial membrane column in reversed-phase liquid chromatography. Journal of Chromatography A 946:107–124. 33. West C., Lesellier E. 2010. Characterization of stationary phases in supercritical fluid chromatography with the solvation parameter model. In Advances in Chromatography, 48, ed. E. Grushka and N. Grinberg, 195–253. CRC Press, Boca Raton, FL. 34. Fuguet E., Ràfols C., Bosch E., Abraham M. H., Rosés M. 2006. Selectivity of single, mixed, and modified pseudostationary phases in electrokinetic chromatography. Electrophoresis 27:1900–1914. 35. Platts J. A., Abraham M. H., Zhao Y. H., Hersey A., Ijaz L., Butina D. 2001. Correlation and prediction of a large blood–brain distribution data set—An LFER study. European Journal of Medicinal Chemistry 36:719–730. 36. Gratton J. A., Abraham M. H., Bradbury M. W., Chadha H. S. 1997. Molecular factors influencing drug transfer across the blood–brain barrier. Journal of Pharmacy and Pharmacology 49:1211–1216. 37. Abraham M. H. 2004. The factors that influence permeation across the blood–brain barrier. European Journal of Medicinal Chemistry 39:235–240. 38. Abraham M. H., Zhao Y. H., Le J., Hersey A., Luscombe C. N., Reynolds D. P., et al. 2002. On the mechanism of human intestinal absorption. European Journal of Medicinal Chemistry 37:595–605. © 2012 Taylor & Francis Group, LLC

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39. Abraham M. H., Martins F. 2004. Human skin permeation and partition: General linear free-energy relationship analyses. Journal of Pharmaceutical Sciences 93:1508–1523. 40. Abraham M. H., Ràfols C. 1995. Factors that influence tadpole narcosis—An LFER analysis. Journal of Chemical Society Perkin Transactions 2:1843–1851. 41. Hoover K. R., Acree W. E., Abraham M. H. 2005. Chemical toxicity correlations for several fish species based on the Abraham solvation parameter model. Chemical Research In Toxicology 18:1497–1505. 42. Hoover K. R., Flanagan K. S., Acree W. E., Jr., Abraham M. H. 2007. Chemical toxicity correlations for several protozoas, bacteria, and water fleas based on the Abraham solvation parameter model. Journal of Environmental and Engineering Science 6:165–174. 43. Poole S. K., Poole C. F. 1996. Model for the sorption of organic compounds by soil from water. Analytical Communications 33:417–419. 44. Abraham M. H., Chadha H. S., Leitao R. A. E., Mitchell R. C., Lambert W. J., Kaliszan R., et al. 1997. Determination of solute lipophilicity, as log P(octanol) and log P(alkane) using poly(styrene–divinylbenzene) and immobilized artificial membrane stationary phases in reversed-phase high-performance liquid chromatography. Journal of Chromatography A 766:35–47. 45. Krass J. D., Jastorff B., Genieser H. 1997. Determination of lipophilicity by gradient elution high-performance liquid chromatography. Analytical Chemistry 69:2575–2581. 46. Valkó K., Plass M., Bevan C., Reynolds D., Abraham M. H. 1998. Relationships between the chromatographic hydrophobicity indices and solute descriptors obtained by using several reversed-phase, diol, nitrile, cyclodextrin and immobilized artificial membranebonded high-performance liquid chromatography columns. Journal of Chromatography A 797:41–55. 47. Miyake K., Kitaura F., Mizuno N., Terada H. 1987. Phosphatidylcholine-coated silica as a useful stationary phase for high-performance liquid chromatographic determination of partition coefficients between octanol and water. Journal of Chromatography A 389:47–56. 48. Valkó K., Du C. M., Bevan C. D., Reynolds D. P., Abraham M. H. 2000. Rapid-gradient HPLC method for measuring drug interactions with immobilized artificial membrane: Comparison with other lipophilicity measures. Journal of Pharmaceutical Sciences 89:1085–1096. 49. Abraham M. H., Chadha H. S. 1996. Applications of a solvation equation to drug transport properties. In Methods and principles in medicinal chemistry. 4. Lipophilicity in drug action and toxicology, ed. B. Testa, H. V. de Waterbeemd and V. Pliska, 311–337. John Wiley & Sons, Weinheim, Germany. 50. Valkó K., Du C. M., Bevan C., Reynolds D. P., Abraham M. H. 2001. Rapid method for the estimation of octanol/water partition coefficient (log P-oct) from gradient RP-HPLC retention and a hydrogen bond acidity term (Sigma alpha(H)(2)). Current Medicinal Chemistry 8:1137–1146. 51. Abraham M. H., Chadha H. S., Leo A. J. 1994. Hydrogen bonding: XXXV. Relationship between high-performance liquid chromatography capacity factors and water–octanol partition coefficients. Journal of Chromatography A 685:203–211. 52. Martel S., Guildume D., Henchoz Y., Galland A., Veuthey J. L., Rudoz S., Carrupt P. A. 2008. Chromatographic approaches for measuring log P. In Methods and Principles in Medicinal Chemistry. 37. Molecular Drug Properties: Measurement and Prediction, ed. R. Manhold, R. Kubinvi, and G. Folkers, 331-355. Wiley-VCH. Weinheim, Germany 53. Shoshtari S. Z., Wen J., Alany R. G. 2008. Octanol–water partition coefficient determination for model steroids using an HPLC method. Letters in Drug Design and Discovery 5:394–400. 54. Canals I., ValkÓ K., Bosch E., Hill A. P., Rosés M. 2001. Retention of ionizable compounds on HPLC. 8. Influence of mobile-phase pH change on the chromatographic retention of acids and bases during gradient elution. Analytical Chemistry 73:4937–4945. © 2012 Taylor & Francis Group, LLC

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55. Canals I., Portal J. A., Bosch E., Rosés M. 2000. Retention of ionizable compounds on HPLC. 4. Mobile-phase pH measurement in methanol/water. Analytical Chemistry 72:1802–1809. 56. Canals I., Oumada F. Z., Rosés M., Bosch E. 2001. Retention of ionizable compounds on HPLC. 6. pH Measurements with the glass electrode in methanol–water mixtures. Journal of Chromatography A 911:191–202. 57. Rived F., Canals I., Bosch E., Rosés M. 2001. Acidity in methanol–water. Analytica Chimica Acta 439:315–333. 58. Espinosa S., Bosch E., Rosés M. 2000. Retention of ionizable compounds on HPLC. 5. pH scales and the retention of acids and bases with acetonitrile–water mobile phases. Analytical Chemistry 72:5193–5200. 59. Bosch E., Espinosa S., Rosés M. 1998. Retention of ionizable compounds on highperformance liquid chromatography. III. Variation of pK values of acids and pH values of buffers in acetonitrile–water mobile phases. Journal of Chromatography A 824:137–146. 60. Espinosa S., Bosch E., Rosés M. 2002. Retention of ionizable compounds in high-performance liquid chromatography IX. Modeling retention in reversed-phase liquid chromatography as a function of pH and solvent composition with acetonitrile–water mobile phases. Journal of Chromatography A 947:47–58. 61. Fuguet E., Ràfols C., Bosch E., Rosés M. 2007. Determination of the chromatographic hydrophobicity index for ionisable solutes. Journal of Chromatography A 1173:110–119. 62. Fuguet E., Ràfols C., Bosch E., Rosés M. 2009. Chromatographic hydrophobicity index: pH profile for polyprotic compounds. Journal of Chromatography A 1216:7798–7805. 63. Espinosa S., Bosch E., Rosés M., Valkó K. 2002. Change of mobile phase pH during gradient reversed-phase chromatography with 2,2,2-trifluoroethanol–water as mobile phase and its effect on the chromatographic hydrophobicity index determination. Journal of Chromatography A 954:77–87. 64. Chitra R., Smith P. E. 2001. Properties of 2,2,2-trifluoroethanol and water mixtures. Journal of Chemical Physics 114:426–435. 65. Espinosa S., Bosch E., Rosés M. 2002. Acid–base constants of neutral bases in acetonitrile–water mixtures. Analytica Chimica Acta 454:157–166. 66. Rosés M., Bosch E. 2002. Influence of mobile phase acid–base equilibria on the chromatographic behavior of protolytic compounds. Journal of Chromatography A 982:1–30. 67. Bosch E., Bou P., Allemann H., Rosés M. 1996. Retention of ionizable compounds on HPLC. pH scale in methanol–water and the pK and pH values of buffers. Analytical Chemistry 68:3651–3657. 68. Pagliara A., Carrupt P., Caron G., Gaillard P., Testa B. 1997. Lipophilicity profiles of ampholytes. Chemical Reviews 97:3385–3400. 69. Karcher S. C., Laufer S. A. 2009. Aza-analogue dibenzepinone scaffolds as p38 mitogen-activated protein kinase inhibitors: Design, synthesis, and biological data of inhibitors with improved physicochemical properties. Journal of Medicinal Chemistry 52:1778–1782. 70. Bartalis J., Halaweish F. T. 2005. Relationship between cucurbitacins reversed-phase high-performance liquid chromatography hydrophobicity index and basal cytotoxicity on HepG2 cells. Journal of Chromatography B 818:159–166. 71. Casartelli A., Bonato M., Cristofori P., Crivellente F., Dal Negro G., Masotto I., et al. 2003. A cell-based approach for the early assessment of the phospholipidogenic potential in pharmaceutical research and drug development. Cell Biology and Toxicology 19:161.

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Recent Developments and Applications in Nonlinear Reversed Phase Liquid Chromatography Nicola Marchetti, Luisa Pasti, Francesco Dondi, and Alberto Cavazzini

Contents 9.1 Introduction................................................................................................... 416 9.2 Models of Nonlinear Chromatography.......................................................... 416 9.2.1 The Ideal Model................................................................................. 417 9.2.2 The Equilibrium-Dispersive Model................................................... 418 9.2.3 The General Rate Model................................................................... 419 9.3 Modeling of Nonlinear Separations: Experimental Determination of Adsorption Isotherms................................................................................ 420 9.3.1 Frontal Analysis................................................................................. 420 9.3.2 Frontal Analysis by Characteristic Point........................................... 421 9.3.3 Elution by Characteristic Point.......................................................... 422 9.3.4 Perturbation Method.......................................................................... 423 9.3.5 Inverse Methods................................................................................. 424 9.3.5.1 Classical Inverse Method.................................................... 425 9.3.5.2 Direct Inverse Method........................................................ 426 9.3.6 Peak Deconvolution in Multicomponent-Overloaded Liquid Chromatography.................................................................... 426 9.4 Applications of Nonlinear Modeling for Characterization of Adsorptive Stationary Phases and Phase Equilibria........................................................ 428 9.4.1 Influence of Mobile Phase pH on the Overloaded Peak Profile........ 429 9.4.2 Chiral Liquid Chromatography under Reversed Phase Conditions.... 430 9.4.3 Nonlinear Behavior with Hydrophobic and Hydrophilic Interaction Elution Mechanisms........................................................ 435 Acknowledgments................................................................................................... 438 References............................................................................................................... 438

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9.1  Introduction High performance liquid chromatography is today the most prominent technique for adsorption study. Studying adsorption equilibria and possibly involved secondary equilibria (i.e., competition for adsorption sites other compounds, organic solvent molecules, employed mobile phase additives, or presence of other batch equilibrium) by dynamic approaches can allow deep investigations on unclear separation mechanisms, as well as finding or developing the right models to describe the chromatographic process under a wide range of sample concentrations (nonlinear chromatography). For many years, this has been strictly related to important fields in academic research, analytical chemistry analysis, and industrial processes. The former studies gave strong impulses to nonlinear chromatography from both theoretical and experimental parts: Various models of chromatography were derived, discussed, validated, and used [1–6]; a large number of isotherm models were developed and applied to fit experimental adsorption data [7–12]; precision and accuracy of different techniques for adsorption isotherm determination were determined and compared [13–16]; numerical and instrumental sources of error during isotherm measurement were found and evaluated in their influence on the correctness of final results [17–19]; new approaches for isotherm determination were developed in perspective of somehow overcoming limits and drawbacks [20,21]; etc. In the next section, the most widely employed models of chromatography will be briefly presented for fundamental aspects of nonlinear chromatography required for understanding how molecules and solute concentrations travel along the column. Then, the principal techniques for isotherm determination will be illustrated. In this part, a couple of recent implementations are also included and discussed. The last section will be focused on applications of nonlinear modeling to study the adsorption equilibria for both chiral and nonchiral separation mechanisms. A conspicuous part will be dedicated to report studies involving secondary acid–base equilibria. The efforts made in order to understand the role of solute ionization (acid–base dissociation) and of the mobile phase pH are displayed. The last part will be dedicated to success models able to bind both information (adsorption and acid–base dissociation equilibrium) and take it into account in one single model.

9.2  Models of Nonlinear Chromatography When scientists started to study the complicated phenomena behind the chromatographic process, the main need was to find useful theoretical expressions to describe at different insight levels and to have a better understanding of the entire separation process. Fluid dynamics, mass transfer phenomena, and equilibrium thermodynamics can be differently enclosed in models, and the relative importance of thermodynamics of phase equilibria and of the kinetics of mass transfer can be modulated as well. Development and studies of such models produced a large amount of knowledge that represents the fundamental theoretical basis of chromatography [22]. © 2012 Taylor & Francis Group, LLC

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9.2.1  The Ideal Model The main hypothesis for this model is that the chromatographic column has an infinite efficiency. Additionally, axial dispersion or mass transfer kinetics are not taken into account at all, as well as the contribution of mobile phase or other processes leading to band broadening. The ideal model assumes that stationary and mobile phases are constantly and instantaneously at equilibrium and it focuses attention on the thermodynamics of phase equilibria as the only factor that influences the peak shape. Under these assumptions, the amount of component i accumulated in a slice δz of the column during the time δt is given by the following differential mass balance equation [22]: ∂Ci ∂q ∂C +F i +u i =0 ∂t ∂t ∂z



(9.1)

where q and C are the solute stationary phase and mobile phase concentrations, respectively u is the mobile phase linear velocity F is the phase ratio t and z are the time and the column length independent variables, respectively Mathematical properties of this equation describe that it propagates discontinuities (or shock) and that a stable concentration shock must take place on the front side of the profile, but also that solution of Equation 9.1 has a continuous or diffuse boundary on the rear side of the profile. This introduces the fundamental aspect of the migration of an injected band and its evolution along the column in nonlinear chromatography. Each mobile phase concentration Ci for component i determines the migration velocity of a given concentration zone, uz,i, and they are associated by u z ,i =

u dq

1 + F dCi



(9.2)

i

This means that the migration velocity depends on the mobile phase concentration Ci and on the local slope of the adsorption isotherm, dqi/dCi (Figure 9.1). Thus, the migration velocity associated with a given concentration zone is constant and each concentration propagates along the column at a constant velocity. In the case of Langmuir-type isotherms (convex upward), dqi/dCi decreases constantly with increasing concentration Ci; hence, uz,i increases with increasing Ci. Therefore, the higher concentrations move faster than the lower concentration; this results in the rear band profile spreading, and a diffuse boundary is formed. On the front side, a concentration discontinuity (shock) develops and this migrates at a velocity inversely proportional to the slope of the isotherm chord from point (C,q) to the origin (see Figure 9.1): us ,i =

u 1+ F

∆qi ∆Ci



(9.3)

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q (mM)

40

dq/dc|c = c

0

30 20

q(c0)/c0

10 0

0

10

20 c (mM)

30

40

Figure 9.1  Graphical meaning of velocity associated with a concentration and velocity of solute molecules. (Adapted from J. Samuelsson et al., Analytical Chemistry 76 (2004) 953.)

This means that if Equations 9.2 and 9.3 are compared for a Langmuir-type isotherm, the migration velocity of a shock of concentration C is smaller than the migration velocity of the same concentration C on the rear part of the band. In the case of a single-component system, the eluted chromatographic profile is calculated by the integration of the differential mass balance equation (Equation 9.1) under proper initial and boundary conditions. These conditions are important to define the exact solution needed and have a clear physical meaning related with the experimental procedure followed [22]. For multicomponent separations, a system of Equation 9.1 (one for each adsorbing component) has to be written and a set of conditions for each component i has to be applied. Although the theory of nonlinear chromatography for multicomponent systems has been extensively studied [23–33], a large number of applications and case studies are still published every year. They will be reviewed here with respect to both chiral and nonchiral aspects.

9.2.2  The Equilibrium-Dispersive Model Another model used for modeling nonlinear separations when the mass transfer kinetics are taken into account is the so-called equilibrium-dispersive model. The differential mass balance equation can be written as



∂Ci ∂q ∂C ∂ 2 Ci + F i + u i = Da ,i ∂t ∂t ∂z ∂z 2

(9.4)

where Da,i is the apparent dispersion coefficient for component i. This model assumes that the Da term lumps all the nonequilibrium contributions leading to band broadening such as molecular diffusion, eddy diffusion, mass-transfer resistances, and finite rate of the kinetics of adsorption–desorption [34]:



Da =

σ 2L 2t0

(9.5)

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where σ 2L is the peak standard deviation in length unit at infinite dilution and t0 the column hold-up time. There are no closed-form solutions of the equilibrium-dispersive model, so Equation 9.4 can be only numerically solved. The most widely applied approach to find numerical solutions for Equation 9.4 is the so-called finite difference method, where the continuous space–time plane is replaced by a discrete grid (Δz, Δt) and the differential equation is replaced by the appropriate difference equation [22]. Finite differences can be written for each term of the differential equation and many combinations of them can be used in order to approximate Equation 9.4 with different finite difference schemes. Other approaches exist to solve differential equations numerically and they are referred to as finite element methods. Here the time–space domain is divided into subdomains (finite elements) wherein a continuous polynomial interpolation is used to approximate the unknown function [35]. Within these methods, the most widely employed is the so-called orthogonal collocation on finite elements (OCFE) [36]. Going back to the finite difference method, two different approaches have been developed to control the error propagation occurring during the numerical calculation of the differential equation solutions. First, the integration elements can be appropriately chosen to minimize the errors [37,38]. Second, the space and time increments are chosen so that the numerical dispersion simulates the band dispersion effect caused by the Da coefficient [39–42]. This approach is applied in Rouchon and Craig algorithms and allows good accuracy of the calculated band profile in the case of a single-component system. Recently, Horvath et al. [43] developed a calculation algorithm based on the Martin–Synge plate model [44] to calculate solutions of the mass balance equation. The authors compared their algorithm (named the Martin–Synge algorithm) with the most frequently used finite difference (Rouchon algorithm) and OCFE methods. In this work, the Martin–Synge algorithm appears to be superior compared with the others because it can still give good results even when other methods are either unstable or not easily implemented.

9.2.3  The General Rate Model The general rate model of chromatography (GRM) is the most comprehensive and complete model. It was developed to account for slow and complex mass transfer kinetics in preparative and nonlinear chromatography because it occurs for large molecules (e.g., peptides and proteins). The aim of the GRM is to consider all the contributions to mass transfer resistance having a strong influence on the band broadening and eluted band profile. This is achieved by means of separate equations describing the kinetics phenomena taking place during the chromatographic process: mass transfer between the percolating mobile phase and the stagnant mobile phase inside the pores molecular diffusion into the stagnant mobile phase molecular diffusion on the adsorbent surface kinetics of adsorption/desorption processes © 2012 Taylor & Francis Group, LLC

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The set of equations involved includes mass balance equations for each of the two different kinds of mobile phases (flowing and stagnant) kinetic equations for the equilibration between the two mobile phases and between the stagnant liquid and the stationary phase suitable boundary and initial conditions The reason why the GRM is much less employed than other models arises from its complicated form and difficulties in its application. Closed-form solutions of the GRM directly exist only in linear chromatography and most efforts were made to find useful expressions in the Laplace domain [45,46]. In nonlinear chromatography, the GRM can be numerically solved with the previously described methods, and it was successfully applied in the past [47,48]. Further discussion and equation development is beyond the aim of this review. Detailed information on this model can be found elsewhere [22].

9.3  M  odeling of Nonlinear Separations: Experimental Determination of Adsorption Isotherms This section reviews the most used methods for conducting measurement of adsorption isotherm. Some of them were deeply investigated and applied since their development quite a long time ago (i.e., frontal analysis, frontal analysis by characteristic point, and elution by characteristic point). These procedures are now accurately known in both their positive and negative aspects. On the other hand, other techniques have been applied quite recently to liquid chromatography (i.e., perturbation method and inverse method), even if the development of their theoretical basis goes back a long time. However, these methodologies are still the objects of implementation. Beyond a short description of the five previously cited techniques, recent developments and case studies will be presented. Some of them have strong im­p­l ications in practical aspects of chemical analysis, as happens for the frontal analysis toward the development of new stationary phases for preconcentration purposes. This is extremely relevant for some branches of analytical chemistry (i.e., environmental analytical chemistry), where advanced techniques of sample treatment and analysis are continuously developed and implemented. The next section will be dedicated to interesting applications of these isotherm determination methods employed to characterize both the adsorptive stationary phase and the involved phase equilibria.

9.3.1  Frontal Analysis Since the frontal analysis (FA) method has developed, its applications to both single and multicomponent systems are numerous. A series of recent works have been reviewed by the same authors of this work [49] with particular emphasis on competitive systems. FA is undoubtedly the most accurate technique for isotherm © 2012 Taylor & Francis Group, LLC

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determination and hence the most employed [22] when specific experimental requirements are fulfilled (see later discussion). During single-component FA measurements, the concentration of a single component is instantaneously changed from Ca to Cb. The chromatographic column is fed with a constant stream of solute at a given concentration up to the point when a breakthrough curve is recorded at the detector. The solute is retained on the chromatographic bed and then eluted as a frontal zone developing a sharp front (shock) at the column outlet. Once the shock front is eluted, a stable plateau zone is reached and the concentration of feeding stream can be changed again back to Ca value. At this point a diffuse rear boundary is produced at the column outlet. Now, the chromatographic system is ready to perform a new FA breakthrough curve, increasing (or decreasing) the solute concentration step. Each FA step represents one single point of the isotherm curve. As a consequence, the FA technique needs a large amount of solute in order to describe the entire adsorption isotherm fully. Additionally, instrument modifications able to reduce the extra column volume considerably, as well as to shorten the solvent delivery channels, are mandatory to perform FA experiments. In a case FA is performed in a step series mode, the breakthrough curve starts and ends at a solute concentration equal to zero and the amount adsorbed in the stationary phase, q(C), in equilibrium with a mobile phase concentration C can be calculated by means of the following equation: q(C ) =

C (VF − VD ) Vads

(9.6)

where VF is the retention volume of the self-sharpening front V D is the system dead-volume (the extra column volume plus the column holdup volume) Vads is the volume of the adsorbent material filling the column Prior to performing this calculation, conversion of profiles from absorbance to concentration units have to be done. This is fulfilled by the detector curve calibration.

9.3.2  Frontal Analysis by Characteristic Point In contrast with FA experiments, where the shock front is required to determine isotherm points, thermodynamic data can also be derived from the concentration profile of the rear boundary of breakthrough curves. This method is called frontal analysis by characteristic point (FACP) and is performed by recording the diffuse profile when the solute concentration is step decreased. Hence, less material is needed than that required by FA experiments. The precision of acquired data is strongly influenced by the finite column efficiency as well as the cumulative characteristic of other errors occurring during the measurements [16,50]. This was found to affect measurements at very low © 2012 Taylor & Francis Group, LLC

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concentrations especially. Also, the FACP method requires a detector calibration curve to convert profiles from absorbance to concentration unit. The isotherm can be reconstructed by the integration of the area under the diffuse rear part of breakthrough curves starting from the tail end (C = 0), as reported in the following expression for a Langmuir isotherm: 1 Vabs



∫

C

0

(V − VD ) dC

(9.7)

9.3.3  Elution by Characteristic Point The method of elution by characteristic point (ECP) employs the rear part of an overloaded band profile, instead of the diffuse tail of a breakthrough curve as for FACP. ECP is based on the same concepts of velocity associated with a concentration and the dependence of this velocity on the isotherm slope (see Equation 9.2). Equation 9.7 can be used for ECP calculations once it is rewritten as  dq  t R (C ) = t0  1 + F dC  



(9.8)

Sources of error made during ECP isotherm estimation have been analyzed [51]. Special attention has to be paid to the column efficiency, the model of isotherm chosen, and the heterogeneity of adsorptive materials (i.e., chiral stationary phases). This results in some constraints that have to be fulfilled when employing the ECP method: Only convex upward (type I) or convex downward (type III) isotherms can be used as adsorption models (the ECP method cannot be applied to any S-shaped isotherm). Column efficiency has to be sufficiently high (the ECP method is based on the ideal model; see Section 9.2.1). Experimental injection profiles have to be as close as possible to the theoretical rectangular shapes. Tubing and connections can be optimized in order to limit the solute diffusion, and hence the extra column contributes to band broadening that is responsible for the loss of efficiency. However, the sampling loop itself and the injection system can make an important contribution to this and also produce dispersed injection profiles very different from quasi-rectangular distributions. Samuelsson and Fornstedt [52] developed a new injection procedure based on cutting off the diffuse tail. Once the sample loop is loaded and the injector is switched, the mobile phase starts to push the sample solution into the column. Before the tail of the injection profile enters the column, the injector is switched back to load position. The amount of injected sample can be calculated from the © 2012 Taylor & Francis Group, LLC

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C/C0

0

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1

1.5

1

Conc (mM)

0.5 0

(b)

50 µL 100 µL 250 µL 500 µL 900 µL

2

4980 µL CUT inj

Conc (mM)

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(a)

0.5 0

0

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2

3 4 Volume (mL)

5

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4980 µL Rectangular

50 0

6

8

100

10

12

14

16

CUT Rectangular

50 0

6

8

10 12 14 Retention Volume (mL)

16

Figure 9.2  Experimental injection profiles (left) for different injection volumes (top) and for cut-injection compared with traditional full-loop injection (down). Chromatograms on the right are the eluted band profiles of methyl mandelate (100 mM) resulting after a traditional full-loop injection (top) and cut-injection (down). (Adapted from J. Samuelsson, and T. Fornstedt, Analytical Chemistry 80 (2008) 7887.)

time that the injector was kept in inject position and from the mobile phase flow rate. The authors demonstrate the improved agreement between experimental and calculated overloaded band profile when using the cut-injection instead of a classical full loop (see Figure 9.2).

9.3.4  Perturbation Method Once a column is equilibrated with a stream of mobile phase at a given concentration of the solute under investigation, injection of a small pulse (perturbation) of a diluted solution of the same component can be performed. According to the concentration feed, the perturbation exhibits a certain retention time. From a set of retention volumes of the perturbation peaks recorded under different solute concentrations in the mobile phase, the adsorption isotherm can be determined. Typically, when the injection of a small excess of a solute is done after the column is equilibrated with increasing concentrations of the same component, the method is called perturbation on a plateau (PP). Description of what happens during PP experiments necessarily is based on the presence of two different peaks (perturbation and mass peaks) and the concept of their different associated velocities. This was explained over 40 years ago by Helfferich and Peterson [53] and Helfferich [54] and the evidence of this hypothesis was presented by Samuelsson et al. in 2004 [55]. If the plateau concentration is within the linear part of the isotherm, perturbation and mass peak move together and have identical retention times. This is related to the fact that, here, chord and tangent of the isotherm coincide and hence the same applies to the associated velocities. In case the plateau concentrations are moderate or large (nonlinear range of the isotherm), the two peaks do not travel at the same velocity along the column. When the isotherm curve is the Langmuir type, the mass peak is eluted after the first positive perturbation peak, but it can exit from the column together with the © 2012 Taylor & Francis Group, LLC

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second negative perturbation peak (vacancy). As a consequence, the mass peak is not detectable because UV-Vis detectors are not able to distinguish the plateau solute from the injected pulse. This issue can be solved by injecting radiochemically labeled molecules and by using a radiochemical detector, or by using a mass spectrometric detector with isotope-labeled molecules. This method is called the tracer pulse (TP) method and allows one to obtain adsorption information from the mass peak of the labeled tracer, whose velocity is related with the corresponding chord of the isotherm curve.

9.3.5  Inverse Methods The inverse method (IM) is one of the existing approaches to measure single- as well as multicomponent competitive adsorption isotherm parameters. Mathematically, IM is based on solving the inverse problem (i.e., iteratively numerical estimation of isotherm parameters until simulated batch separations are in satisfactory agreement with actual experimental results [56–58]). In other words, IM consists of optimizing the isotherm parameters by minimizing the differences between one (or several) experimental nonlinear chromatographic peaks and the corresponding profiles obtained by solving a proper model of nonlinear chromatography. Compared with the classical techniques previously described (FA, FACP, ECP, or PM), IM requires little experimental effort and a small amount of material. Although IM has been applied in several studies with different isotherm models, some drawbacks can be evidenced. The first is related to the detector signal (usually an UV detector) that requires calibration. Second, the adsorption isotherm model has to be chosen a priori before performing the calculation. This fact implies that a careful statistical analysis on the significance of the isotherm parameters has to be performed to sustain a chosen model and a comparison between different adsorption models is mandatory. An innovative approach, called direct inverse method (DIM), was described recently as a valid alternative to classical IM [59]. Calculations in DIM, derived by the classical IM, are based on elution profiles at multiple wavelengths. When components coelute out the chromatographic column, classical IM can be applied in two different ways: (1) fraction collection and consequent analysis of these fractions, and (2) use of calibration data and simulated profiles to estimate the detector response and to fit this to the experimental signals. Both approaches require UV detector calibration for each component at one or multiple wavelengths. DIM overcomes these limitations since it does not require calibration and it can be used even in case of severe overlapping between components without necessity of fraction collection. Limitations of DIM are either common to classical IM (i.e., estimated isotherm parameters are accurate only up to the concentration levels reached at the column outlet during measurements acquired for parameter estimation) or typical of the proposed method (i.e., it can be used only in the case of enantiomers). The main assumption made for DIM is that the measured UV profiles are linearly proportional with the solute concentration for all the involved components. This limits the applicability of DIM to a certain range of wavelengths. On the other hand, the method is calibration free and does not require the pure components to be available. © 2012 Taylor & Francis Group, LLC

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The measured signal intensity at a certain wavelength λ and at a given time t, x(t, λ) can be expressed as a linear combination of the signal corresponding to each component (1,…,d): d

x (t , λ) =

∑ c (t)a (λ) + e(t, λ) l

l

(9.9)

l =1

where

al(λ) represents the intensity at wavelength λ of the pure component spectrum corresponding to the lth component cl(t) denotes the concentration of the lth component at time t e(t, λ) is the experimental error (i.e., noise interference, nonidealities of the measurements, etc.) Equation 9.9 can be rewritten using the matrix notation when discrete spectral and time coordinates are employed: ˆ +E X = CA + E = X



(9.10)

being Xˆ , the modeled spectral matrix, whose elements xi,j are the jth calculated intensity for the ith sample. C represents the state matrix, where the lth column is the discretized concentration profile in time of the lth component. The lth row in matrix  denotes the discretized pure component spectrum for component l. 9.3.5.1  Classical Inverse Method The basic procedure to apply IM calculations for isotherm determination can be depicted in the following steps:

1. Choose an adsorption isotherm model. 2. Choose the model of nonlinear chromatography to apply. 3. Compare the numerical solution of the differential mass balance equation and the experimental elution peaks. 4. The isotherm parameters are changed to minimize these differences. 5. New numerical solutions are calculated and the isotherm parameters are iteratively changed until the error falls within the desired error limit. 6. Possibly, the entire procedure is repeated with a different isotherm and a statistic comparison between models is evaluated.

The fundamental requirement for the classical IM is the UV detector calibration. This is mandatory for conversion of time evolution of intensity signals (for one wavelength) into the time evolution of the concentration (of one component). In the case of a multicomponent system, once the calibration factors are determined for all the components, the measured state matrix C can be obtained by placing the column © 2012 Taylor & Francis Group, LLC

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vectors next to each other. Based on the chosen model (step 2) of nonlinear chromaˆ (k) can be obtained. k is a tography, a modeled time-resolved concentration matrix C vector containing the model parameters that are physicochemical or transport properties of the system (adsorption isotherm parameters of dispersion coefficients). The classical IM estimated the model parameters by minimizing the difference between the matrices Cˆ (k) and C. 9.3.5.2 Direct Inverse Method This approach uses the X itself (containing the time-resolved UV elution spectra) to estimate the isotherm model parameters directly. This means that conversion of the spectral X matrix into the measured concentrations C matrix is not involved. In other words, the problem is to build the residual matrix R(k) and to minimize the sum of the squares of its elements ri,j: ˆ (k ) A R (k ) = X − C



(9.11)

where Cˆ (k) is the calculated state matrix and the vector k is the unknown variable whose elements are the model isotherm parameters. This can be more easily ˆ + (k) = (C ˆ T (k)C ˆ (k))−1 C ˆ T (k), ˆ (k) (i.e., C achieved using the pseudo-inverse matrix of C so that Equation 9.11 can be rewritten as

ˆ (k)C ˆ + (k)]X ˆ (k)C ˆ + (k ) X = [I − C R (k ) = X − C

(9.12)

9.3.6  P  eak Deconvolution in MulticomponentOverloaded Liquid Chromatography The problem concerning the lack of applicability of classical IM when multicomponent separations are involved was recently studied and faced [60,61] under both isocratic and gradient conditions. The tedious problem of fraction collection and analysis was overcome by the development of an instrumental method for automated online fraction analysis providing for an easier and reliable peak deconvolution. The proposed approach is based on an easy-to-use and inexpensive instrumental setup that involves a switching two-position valve and a sampling loop in between two chromatographic columns. The first provides for overloaded profile separation, while the second receives small pulses from the collected fractions, separated under linear conditions. Two detectors can be employed in order to acquire profiles out of both columns and overlap overloaded bands and linear pulses. The proposed instrumental setup involved two chromatographic columns: a 15 cm long C18 column and a 5 cm long C8 column of the same type and by the same manufacturer. Additionally, the long column 1 was operated at low flow rates (0.1 mL/min) and injections of large volumes of high-concentrated solutions were performed through loops of 100–500 μL, while high flow rates and a 20 μL loop were employed with the short column 2. The method was validated under isocratic reversed phase conditions with two-component © 2012 Taylor & Francis Group, LLC

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λ = 250 nm

Abs (mAU)

2500 2000 1500 1000 500 0 30

35

40

45 50 Time (min)

55

60

65

41.5

42

Abs (mAU)

800 600 400 200

C (g/L)

0

8 7 6 5 4 3 2 1 0

39

39.5

40

40.5 41 Time (min)

AcBz Phe

3

3.5

4

4.5 V (mL)

5

5.5

6

Figure 9.3  Validation of online fraction analysis for a two-component overloaded mixture. Injected concentrations: benzyl alcohol 18.81 g/L, phenol 22.58 g/L. Injection volume: 100 μL. Adapted from V. Costa et al., Journal of Chromatography A 1217 (2010) 4919.)

(benzyl alcohol and phenol; Figure 9.3) and three-component mixtures (benzyl alcohol, phenol, and 2-phenyl-ethanol; Figure 9.4). The validation parameter was the relative error when the nominal injected mass and the calculated mass after peak deconvolution are compared. Two constraints have to be satisfied when operative parameters are chosen (flow rates, sampling time interval, mobile phase composition, etc.): the chromatographic resolution (the ratio between the difference in retention times for two adjacent peaks and four times the average peak standard deviation) and Rs cannot be lower than unit to integrate singlecomponent peaks correctly. Recently, this automated instrumental approach was employed to deconvolute overloaded band profiles of the same binary mixtures (benzyl alcohol and phenol) under gradient elution conditions [61]. Five different levels of gradient steepness © 2012 Taylor & Francis Group, LLC

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λ = 250 nm

Abs (mAU)

2500 2000 1500 1000 500 0

35

40

45

50 55 60 Time (min)

800

65

70

75

200

600 400

100

200 0 40

40.5

41

41.5

42

0 53

53.5

54

10

55

AcBz Phe PhEt

8 C (g/L)

54.5

6 4 2 0

3

4

5

V (mL)

6

7

8

Figure 9.4  Validation of online fraction analysis for a three-component overloaded mixture. Injected concentrations: benzyl alcohol 6.13 g/L, phenol 6.30 g/L, 2-phenylethanol 6.18 g/L. Injection volume: 500 μL. (Adapted from V. Costa et al., Journal of Chromatography A 1217 (2010) 4919.)

were investigated by changing the gradient time. The available sampling window and the sampling frequency constraint are the most critical variables influencing the relative error associated with the mass balance.

9.4  Applications of Nonlinear Modeling for Characterization of Adsorptive Stationary Phases and Phase Equilibria Both classical and newly implemented approaches to determine adsorption isotherms in liquid chromatography reviewed here are most often employed nowadays with multicomponent mixtures. This originates from specific needs in both industrial and academic research to solve problems related with purification steps, development of new stationary phases, or investigation of interactions © 2012 Taylor & Francis Group, LLC

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between solutes and separation media and role of experimental variables (e.g., mobile phase additives, organic solvent content, etc.). Typical complex mixtures are originated by industrial processes where, for instance, a nonchiral compound is required to be purified from a gross reaction mixture. Otherwise, multicomponent mixtures can involve enantiomers that need to be purified and also separated between them in order to isolate a potentially active pharmaceutical product from its enantiomer, which is usually nonactive or even dangerous (e.g., cytotoxic). Single component adsorption data are usually determined to make separation mechanisms clear, investigate how a single molecule type behaves under nonlinear chromatographic conditions, or evaluate behavior and characteristics of the stationary phase (heterogeneity, copresence of selective and nonselective adsorption sites, etc.). On the other hand, competitive modeling is applied to study how adsorption can change as function, for example, of mobile phase pH, other additives’ concentration, organic modifier content, and presence of other competitive molecules.

9.4.1  Influence of Mobile Phase pH on the Overloaded Peak Profile Recently, the elution of neutral and ionic species was analyzed by Gritti and Guiochon [62–64] with respect to the pH of the buffered mobile phase. They experimentally evidenced that elution time and peak shape of ionizable compounds at low compound and buffer concentration are strongly influenced by the pH of the buffered mobile phase. All the illustrated experimental results show that the solute in ionized form is eluted faster than the same molecules in conjugated neutral form. This is consistent with the elution of charged molecules under reversed phase conditions. The role of the mobile phase can be reviewed because its pH does not control the elution time but rather the form of the species that is eluted (acidic, neutral, or basic). Then, the nonlinear behavior of different solutes at various pHs and silicabased C18 stationary phases was also investigated. For small and polar molecules, which do not contain any large hydrophobic moieties, the overloaded peak profiles have a Langmuirian behavior when the pH of the mobile phase is sufficiently higher or lower than pKa of the eluted compound. The authors relate the peak tailing with the overloading of the adsorption sites having the highest energy. These types of sites are present at low concentration on the adsorbent surface and are accessible to the analyte molecules through discontinuities of the C18 bonded layer [65] when the molecule size matches the access point. This is the reason why these sites fill more rapidly than the low-energy sites on the C18 layer, which are present at a high concentration. As a result of this, low mobile phase concentrations are enough to saturate highenergy sites and give peak tailing. In contrast with this, when the compound is in neutral form, its molecules adsorb on low-energy sites, which have a large saturation capacity. The explanation given is the only plausible interpretation of the strong peak tailing exhibited in experimental profiles at low retention times: large equilibrium constants coupled with a small saturation capacity. Another important result of this study concerns the chemical nature of packing material. It is well known that residual silanols on the surface of silica-based © 2012 Taylor & Francis Group, LLC

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particles have a pKa value between 5 and 7, which can be raised up to 10 when methyl groups are inserted in the silica matrix. Since these points represent the high-energy sites responsible for remarkable peak tailing, different manufactured packing material can be compared. Four different stationary phases are evaluated, divided into two clusters on the basis of a comparable silica surface (square meters per gram). In each group, one stationary phase is purely silica based, while the other has a hybrid inorganic–organic surface. The more peak tailing is observed, the more compound molecules can have access to the high-energy sites on the particle surface. However, peak tailing is not the only parameter to be considered. When basic compounds are injected into the column and eluted with mobile phases at different pH, pure silica-based particles produce a significant increase of retention times when the pH is varied from 2 to 6, even though the end-capping procedure has been done. This variation is limited when hybrid inorganic–organic surface particles are employed because free silanols are here less acidic than on pure silica surfaces. Once sufficiently clear explanation for this was developed, the authors faced the problem of modeling these separations under nonlinear conditions. Isotherm parameters were estimated by the inverse method and then the equilibriumdispersive model was used to calculate the peak profiles. A single-component Langmuir isotherm was used to fit experimental peaks eluted at different mobilephase pH, distant from the solute pKa (see Figure 9.5). When the mobile phase pH is close to the solute pKa, both the acidic and basic species do coexist in the bulk mobile phase. Although this problem is well known in linear chromatography, it was faced in this study with respect to the nonlinear modeling. The first tentative model of the adsorption isotherm was still the single component Langmuirian case, but now the equilibrium constant is a function of the local mobile phase concentration. A coefficient α can be used to indicate the ratio between the mobile phase concentration of neutral species and the total mobile phase concentration. A two-site noncompetitive adsorption model was finally employed for modeling the separation in the whole pH range (2.6–8.6). This model assumes a heterogeneous adsorbent surface, covered with two types of adsorbing sites. One has a very small saturation capacity and a very large equilibrium constant (for ionized species); the other one has a large saturation capacity and a small equilibrium constant (for neutral species). The agreement between the experimental profiles and those calculated by this last model was satisfactory and few changes of parameters were required to improve the goodness of fit.

9.4.2  Chiral Liquid Chromatography under Reversed Phase Conditions Recent applications and studies of the enantiorecognition mechanism involve chiral stationary phases (CSPs) that can be operated under reversed phase conditions (donor–acceptor or Pirkle-type CSP [66–70], carbamate-based CSP [71], and protein immobilized based [72]). An aqueous/organic buffered mobile phase always represents the best choice, when possible, in the liquid chromatographic purification of pharmaceutical products. Before it was discovered that some CSPs allow © 2012 Taylor & Francis Group, LLC

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0.3 0.2

C (g/L)

C (g/L)

0.4

pH = 6.5

0.1

0.3

pH = 2.6

0.2 0.1

0.0 75

150 Time (s)

0.0

225

0.3

0.3

0.2

0.2

C (g/L)

C (g/L)

0

pH = 8.6

0.1 0.0 0

75

150 Time (s)

225

0

75

150 Time (s)

225

150 Time (s)

225

pH = 4.5 0.1 0.0

0

75

Figure 9.5  Comparison between calculated and experimental band profiles of aniline at different mobile phase pH. (Adapted from F. Gritti, and G. Guiochon, Journal of Chromatography A 1216 (2009) 63.)

enantioseparation under reversed phase conditions, pharmaceutical industries had to face the problem of solvents used in normal phase. On the one hand, the possibility of operating chiral purification with acidic or buffered aqueous-organic mobile phase gives a strong impulse to these CSPs. On the other hand, retention mechanisms under nonlinear conditions and separation modeling of chiral ionizable compounds have to be investigated. In 2010 Asnin et al. [66], Asnin, Horvath, and Guiochon [67], and Asnin and Guiochon [68–70] conducted several detailed studies on the enantioselective characteristic of Whelk-01 CSP (Pirkle-type CSP) toward a weak acidic chiral compound (Naproxen) under nonlinear and aqueous-organic mobile phase conditions. Also, the behavior of this CSP toward the adsorption of water or organic modifier, additives in mobile phase, and column temperature was investigated. The adsorption of water– methanol mixtures (employed mobile phases) on the Whelk-01 CSP was studied by means of total and excess isotherms. Results evidenced that, for the entire range of solution composition, methanol has a positive adsorption on this stationary phase, while it is negative for water. This means that the CSP preferably adsorbs methanol instead of water (the concentration of methanol in the adsorbed layer on the CSP is larger than in the bulk mobile phase, while water concentration is lower on the CSP than in bulk); hence, the CPS surface is relatively hydrophobic. © 2012 Taylor & Francis Group, LLC

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Investigations continued with the nonlinear behavior of Naproxen enantiomers on this CSP. The authors determined the adsorption isotherms for three different mobile phase compositions by FA and compared them with those calculated with the IM. Conventional adsorption plots do not reveal the existence of small deviations of experimental data from a simple Langmuir model. However, more information can be derived when the same data are plotted as so-called Scatchard coordinates (local isotherm slope vs. adsorbed amount). Scatchard plots show higher curvature than that accounted for in the Langmuir model, particularly for the less methanol-rich mobile phase. For this reason, IM calculations were done with the improved two-site and threesite Langmuir isotherms. Both the curves seemed to fit well the FA data on the conventional plot, while the Scatchard coordinates showed that the tri-Langmuir model was much better than the bi-Langmuir. However, the derived adsorption data and the analysis of breakthrough curves bear out the authors’ idea of choosing different models for the two Naproxen enantiomers. Both isotherms are based on the hypothesis of three different adsorption sites: two types of enantioselective site, one at a high-energy and the other at a low-energy level, and one nonselective site at high energy. (R) and (S) enantiomers interact differently with these sites and, for the former, all three types contribute to the adsorption in a specific way, while for the latter the high-energy enantioselective and the nonselective sites can be lumped together so that the tri-Langmuir isotherm (which is required to better describe the nonlinear behavior of (R)-Naproxen) simplifies to a bi-Langmuir model for (S)-Naproxen [69]. The nonmonotonic relationship between the isotherm coefficients and the mobile phase composition suggested to the authors the influence of secondary equilibria on adsorption. Another study [70] investigated the role of the buffered mobile phase on Whelk-01 CSP with (R)- and (S)-Naproxen in order to evaluate the influence of solute dissociation on the chromatographic behavior. This type of study is quite similar to those employed by Gritti and Guiochon [62–64] that were reviewed in the previous subsection: the role of solute acid–base equilibria in nonlinear liquid chromatography. The common aspect between Gritti’s and Asnin’s work is the investigation of nonlinear adsorption of compounds that undergo acid–base dissociation equilibrium during the liquid chromatographic process. Asnin employed buffered and unbuffered mobile phases to modify Naproxen dissociation and test different buffer capacities. This topic can be introduced by considering the different effect of the mobile phase on the solute: (1) Unbuffered acidic solution suppresses the dissociation of weak acidic solutes, while (2) buffered mobile phases can control the degree of dissociation by their working pH and buffering capacity. Hence, one can expect that in the second case two species are involved in the chromatographic process and each of them moves along the column with its own velocity. On the other hand, the two chromatographic bands are correlated by means of the dissociation equilibrium. Typical overloaded Langmuirian band profiles are obtained with unbuffered mobile phases employing acetic acid 0.01 M as an additive (see Figure 9.6a, d). Buffered mobile phases give band profiles totally different from the former case and peak shapes strongly depend on the buffer capacity (i.e., buffer concentration) (see Figure 9.6b, c, e, f). The pH of column out-stream was monitored after the diode array detector with a micro-pH electrode connected to a flow cell. © 2012 Taylor & Francis Group, LLC

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(a)

(d)

(R)-Naproxen

12 Buffer AcOH 0.01 M

8

8

c (mM)

16

c (mM)

(S)-Naproxen

12

Buffer AcOH 0.01 M

4 4 0

5.0

5.5

6.0

6.5

0

7.0

7

(b)

20

(e)

(R)-Naproxen

c (mM)

c (mM)

12 Buffer AcOH 0.01 M AcONa 0.01 M

8 4

5.0

5.5

6.0

6.5

Buffer AcOH 0.01 M AcONa 0.01 M

0

7.0

7

(c)

8

9

10

Time (min)

(f)

(R)-Naproxen

(S)-Naproxen

12

12 8

c (mM)

c (mM)

(S)-Naproxen

4

16

Buffer AcOH 0.03 M AcONa 0.03 M

4 0

10

8

Time (min) 20

9

12

16

0

8 Time (min)

Time (min)

8 Buffer AcOH 0.03 M AcONa 0.03 M

4

0 5.0

5.5

6.0 Time (min)

6.5

7.0

7

8 9 Time (min)

10

Figure 9.6  Effect of unbuffered (top chromatograms) and buffered (middle chromatograms 0.01 M, and down chromatograms 0.03 M) mobile phase on elution of Naproxen enantiomers ((R), left chromatograms, (S), right chromatograms) from different sample concentrations (from 0.22 to 43.4 mM). (Adapted from L. Asnin, and G. Guiochon, Journal of Chromatography A 1217 (2010) 7055.)

The results clearly evidenced a reduction in pH coupled with band elution, and the pH drop is much larger in the case of 0.01 M acetic buffer than for a threefold higher buffer concentration (0.03 M). The buffer capacity in the former case is not large enough to contrast local acidification due to the solute elution when solute concentration is larger than 0.01 M and the magnitude of pH perturbation is higher than with high buffer concentration. © 2012 Taylor & Francis Group, LLC

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The resulting retention in such a system depends obviously on the mobile phase pH and on the partial adsorption isotherms of species involved in acid–base equilibrium. The partial adsorption isotherms are determined by a varied PM and a set of data (VR′ (c)vs. c) are obtained; VR′ (c) is the reduced retention volume of the peak apex, related with the solute mobile phase concentration at the apex: dq(c) VR (c) − V0 = = VR′ (c) c Va



(9.13)

where V0 is the column hold-up volume and Va the volume of the stationary phase. The reduced retention volume, hence, is in relationship with the amount adsorbed, calculated by integration of the function dq(c)/c once the preceding procedure is repeated for increasing sample concentration (see Figure  9.7). It has to be noted that this calculated adsorption isotherm is actually an apparent isotherm, since one of the requirements of the applied pulse method (formally named the Glueckauf method [73–74]) is the chemical integrity of the eluted 40 30

2.4

qr (mM)

VR (ml)

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2.2

20

2.0

10

1.8 0

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8 12 Ca?? (mM)

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8 12 Cr (mM)

(a)

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10

2.8 0

2

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6 8 10 Ca?? (mM) (b)

12

14

0

0

4

8 Cr (mM) (d)

12

16

Figure 9.7  Partial adsorption isotherms (left) and apparent total isotherms (right) for (R)and (S)-Naproxen (top and down, respectively). (Adapted from L. Asnin, and G. Guiochon, Journal of Chromatography A 1217 (2010) 7055.) © 2012 Taylor & Francis Group, LLC

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compound. This is obviously not fulfilled because the pH perturbation in the solute band depends on a sample concentration; then, chromatographic bands of different sample size move along the column and are subjected to different local ionic environment. Now, the authors improved the two different models for the two enantiomers, taking into account the dissociation equilibrium. c(1 – α) and cα are considered the mobile phase concentrations of undissociated Naproxen and its conjugated base, respectively, into bi-Langmuir isotherm for the (S) enantiomer and into the Langmuir–Moreau model for the (R) enantiomer. Calculated overloaded band profiles by the IM are in very good agreement with experimental chromatograms and indicate that the calculation accuracy is comparable with that of the Glueckauf (pulse) method used to measure the adsorption isotherms. Before Gritti and Guiochon [62–64], other authors [72] started to investigate the nonlinear chromatographic behavior of neutral (methyl mandelate), acidic (2-phenylbutyric acid), and basic (alprenolol and 1-(1-naphthyl)ethylamine) chiral compounds as a function of the mobile phase pH. The frontal analysis approach was used for measuring the adsorption isotherms of these compounds on CHIRAL-AGP CPS. This stationary phase consists of α1-acid glycoprotein immobilized onto silica particles. Nonlinear studies were frontal analysis measurements; after that, the chromatographic behavior under linear conditions was evidenced. In general, nonlinear investigations show that the CSP surface was heterogeneous for all the compounds, with a small number of strong enantioselective adsorption sites and a large number of weak nonselective ones. The results for specific behavior reveal that the retention time increasing for basic compounds when increasing the mobile phase pH is based on a strong rise of the enantioselective binding strength. For the neutral compound, the small increase in retention is associated with an increase in both the enantioselective binding strength and the saturation capacity for chiral sites. Finally, in the case of an acidic compound, the retention first increases and then decreases when the pH is incremented. This is due only to the enantioselective interactions: The maximum retention seems to come from a large increment in chiral binding energy while the nonselective energy rapidly drops. Additionally, nonlinear results indicate that for basic compounds, ionic interaction can be very important for the enhancement of enantioselective binding with proteinbased CSP, since the molecule hydrophobicity alone has no significant role in the chiral interaction. The increase of enantioselective binding energy is much greater than for nonselective interaction when the mobile phase pH is raised, although this is true in general for all the analyzed components.

9.4.3  Nonlinear Behavior with Hydrophobic and Hydrophilic Interaction Elution Mechanisms In this section, applications based on two liquid chromatography mechanisms (hydrophobic interaction [HIC] and hydrophilic interaction [HILIC]), different from reversed phase conditions, are discussed. HIC is a separation process driven by entropy in which selective solute retention is based on the interaction between the hydrophobic resin (stationary phase) and nonpolar hydrophobic moieties of the solute molecule. © 2012 Taylor & Francis Group, LLC

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1

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0

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40 Time (min)

60

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Big Chap Concentrations (mM)

Protein Concentrations (mM)

Since its development, HIC has been shown to allow the successful separation of proteins from complex mixtures [76]. Many efforts and theoretical developments have been undertaken for the understanding of adsorption mechanisms in HIC systems—mainly, solvophobic theory [77] and preferential interaction theory [78]. A more recent adsorption isotherm model, called preferential interaction quadratic (PIQ), was applied to describe the effect of mobile phase additives (i.e., salts) on linear and nonlinear adsorption of proteins and small molecules in HIC systems [79]. Furthermore, a new thermodynamic description of adsorption on HIC resin has been proposed in terms of water displacement and ligand density and type [80]. Nagrath, Xia, and Cramer [81] employed the general rate model to characterize an HIC system and to predict both displacement and gradient protein separation (see Figure 9.8). The author determined the transport parameters of proteins through HIC resins and performed frontal experiments to obtain adsorption data for proteins and displacer. The general rate model coupled with the PIQ isotherm was able to describe both the preparative HIC system and linear gradient separation. HILIC describes the mode for separation of polar compounds generally from aqueous solution of acetonitrile, with high acetonitrile concentration. The aqueous mobile phase forms a water-rich layer on the surface of the polar stationary phase. Solutes are distributed between these two layers as in a liquid–liquid partitioning system [82]. However, the retention of solutes in HILIC is not just a simple liquid–liquid partitioning and it may be due to the combination of adsorption and liquid–liquid partition mechanism [83]. The water-rich layer above the surface governs the mixed mode retention of polar compounds under HILIC conditions. The higher the organic

0

Figure 9.8  Modeling of HIC displacement chromatography for proteins (lysozyme [squares] and lectin [circles]) and displacer (triangles). (Adapted from D. Nagrath, F. Xia, and S. M. Cramer, Journal of Chromatography A 1218 (2011) 1219.) © 2012 Taylor & Francis Group, LLC

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800 700 Abs (mAU)

600 500 400 300 200 100 0

0

5

10 Time (min)

15

20

Figure 9.9  (See color insert.) Series of overloaded band profiles of proline (4 g/L) eluted from HILIC column. (Adapted from P. Vajda, A. Felinger, and A. Cavazzini, Journal of Chromatography A 1217 (2010) 5965.)

Г (cm3)

modifier concentration is, the stronger is the repulsion of the polar analytes from the aqueous-organic bulk mobile phase and the retention volumes increase [84]. In a recently published work [85], the nonlinear behavior of a polar analyte (proline) under HILIC conditions from aqueous solutions of acetonitrile was investigated (see Figure 9.9). Additionally, the influence of preferential water adsorption on the silica surface on the adsorption equilibria of proline was determined by means of excess isotherm determination. Water perturbations injected into the column were recorded at a different mobile phase composition (from 0% to 100% v/v of water in acetonitrile). The excess isotherms of water on the HILIC stationary phase (Figure 9.10) were measured with the so-called minor disturbance method [86,87] and were calculated when the mobile phase composition was expressed by volume fraction (black symbols, Figure 9.10) or by molar fraction (red symbols, Figure 9.10). 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 –0.05 –0.1

vNA nNA

0

0.6 0.8 0.2 0.4 H2O Concentration (v/v%)

1

Figure 9.10  (See color insert.) Excess isotherms on porous HILIC column calculated using both volume fraction convention (vNA, black circles) and molar fraction convention (nNA, red circles). (Adapted from P. Vajda et al., Journal of Chromatography A 1217 (2010) 5965.) © 2012 Taylor & Francis Group, LLC

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The two results were compared [85] and reveal that the maximum excess amount of water can be observed at around 20% v/v. Although the calculation of the excess amount through the molar fraction is more exact than that using the volume fraction, the two isotherms have quite similar shapes and comparable locations of maximum positive excess. Adsorption data for proline were obtained through frontal analysis. The isotherm shape clearly corresponds to the type III curve and was modeled with the BET equation: q=

qs bs C (1 − bL C )(1 − bL C + bs C )

(9.14)

where qs is the column saturation capacity bs is the equilibrium constant of the interaction between solute molecules and the surface bL is the equilibrium constant of the interaction between the molecules in the adsorbed layers Isotherm parameters were estimated at different acetonitrile concentrations in the mobile phase (from 70% to 85% v/v). The saturation capacity shows a maximum at 80% of acetonitrile (20% v/v of water) and this is in good agreement with the excess isotherm. The two equilibrium constants (bs and bL) behave similarly and decrease rapidly from higher acetonitrile content until 80% v/v and then moderately at lower acetonitrile concentration.

Acknowledgments This work has been supported in part by grant RBPR05NWWC_008 (CHEMPROFARMA-NET) of the Italian University and Scientific Research Ministry and in part by European funding for the Emilia Romagna Region (POR-FESR 2007-2013) and the High Technology Network (Technopole of Ferrara, Terra & Acqua Tech Laboratory).

References

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49. N. Marchetti, A. Cavazzini, L. Pasti, F. Dondi, Journal of Separation Science 32 (2009) 727. 50. H. Guan, J. B. Stanley, G. Guiochon, Journal of Chromatography 659 (1994) 27. 51. L. Ravald, T. Fornstedt, Journal of Chromatography A 908 (2001) 111. 52. J. Samuelsson, T. Fornstedt, Analytical Chemistry 80 (2008) 7887. 53. F. Helfferich, D. Peterson, Science 142 (1963) 661. 54. F. Helfferich, Journal of Chemical Education 41 (1964) 411. 55. J. Samuelsson, P. Forssen, M. Stefansson, T. Fornstedt, Analytical Chemistry 76 (2004) 953. 56. F. James, M. Sepulveda, Inverse Problems 10 (1994) 1299. 57. A. Felinger, A. Cavazzini, G. Guiochon, Journal of Chromatography A 986 (2003) 207. 58. A. Felinger, D. Zhou, G. Guiochon, Journal of Chromatography A 1005 (2003) 35. 59. J. Cornel, A. Tarafder, S. Katsuo, M. Mazzotti, Journal of Chromatography A 1217 (2010) 1934. 60. A. Cavazzini, V. Costa, G. Nadalini, F. Dondi, Journal of Chromatography A 1137 (2006) 36. 61. V. Costa, L. Pasti, N. Marchetti, F. Dondi, A. Cavazzini, Journal of Chromatography A 1217 (2010) 4919. 62. F. Gritti, G. Guiochon, Journal of Chromatography A 1216 (2009) 63. 63. F. Gritti, G. Guiochon, Journal of Chromatography A 1216 (2009) 1776. 64. F. Gritti, G. Guiochon, Journal of Chromatography A 1216 (2009) 3175. 65. K. A. Lippa, L. C. Sander, R. D. Mountain, Analytical Chemistry 77 (2005) 7852. 66. L. Asnin, F. Gritti, K. Kaczmarski, G. Guiochon, Journal of Chromatography A 1217 (2010) 264. 67. L. Asnin, K. Horvath, G. Guiochon, Journal of Chromatography A 1217 (2010) 1320. 68. L. Asnin, G. Guiochon, Journal of Chromatography A 1217 (2010) 1709. 69. L. Asnin, G. Guiochon, Journal of Chromatography A 1217 (2010) 2871. 70. L. Asnin, G. Guiochon, Journal of Chromatography A 1217 (2010) 7055. 71. R. Arnell, P. Forssen, T. Fornstedt, R. Sardella, M. Lammerhofer, W. Lindner, Journal of Chromatography A 1216 (2009) 3480. 72. G. Gotmar, N. R. Albareda, T. Fornstedt, Analytical Chemistry 74 (2002) 2950. 73. E. Glueckauf, Journal of Chemical Society (1947) 1302. 74. E. Glueckauf, Discussions of Faraday Society 7 (1949) 199. 75. S. L. Lanin, M. Y. Ledenkova, Y. S. Nikitin, Mendeleev Communications 10 (2000) 37. 76. M. M. Diogo, J. A. Quieiroz, G. A. Monteiro, S. A. M. Martins, G. N. M. Ferreira, D. M. F. Prazeres, Biotechnology and Bioengineering 68 (2000) 576. 77. C. Horvath, W. Melander, I. Molnar, Journal of Chromatography 125 (1976) 129. 78. T. Arakawa, S. N. Timasheff, Biochemistry 23 (1984) 5912. 79. F. Xia, D. Nagrath, S. M. Cramer, Journal of Chromatography 989 (2009) 47. 80. R. W. Deitcher, J. E. Rome, P. A. Gildea, J. P. O’Connell, E. J. Fernandez, Journal of Chromatography A 1217 (2010) 199. 81. D. Nagrath, F. Xia, S. M. Cramer, Journal of Chromatography A 1218 (2011) 1219. 82. A. J. Alpert, Journal of Chromatography A 499 (1990) 177–196. 83. P. Jandera, Journal of Separation Science 31 (2008) 1421. 84. F. Gritti, A. dos Santos Pereira, P. Sandra, G. Guiochon, Journal of Chromatography A 1217 (2010) 683. 85. P. Vajda, A. Felinger, A. Cavazzini, Journal of Chromatography A 1217 (2010) 5965. 86. Y. V. Kazakevich, R. LoBrutto, F. Chan, T. Patel, Journal of Chromatography A 913 (2001) 75. 87. Y. V. Kazakevich, H. M. McNair, Journal of Chromatographic Science 31 (1993) 317.

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Index A Abraham columns, 389 Abraham solvation parameter model, 386, 392 Absolute configuration modulation infrared spectroscopy (ACMIS), 58, 84 Absorption, distribution, metabolism, excretion, and toxicity, see ADMET behavior Acetonitrile, 126, 398 Acronyms chiral discrimination, polysaccharide phases, 86 organic monolith column technology, capillary liquid chromatography, 274–275 ADMET behavior, 378 ADMPC (amylose tris(3,5-dimethylphenylcarbamate)) CDMPC comparison, 79 dry PS sorbents, 63, 65 enantioselectivities, 74 fundamentals, 50 liquid state NMR, 60 literature studies, 80–84 PPA with three sorbents, 74 research strategies, 53 sorbent/solvent interactions, 68, 71–72 Adsorption and adsorption conditions, 2, 7 Adsorption isotherms characteristic point, 421–423 classical inverse methods, 425–426 direct inverse methods, 426 elution, 422–423 frontal analysis, 420–422 fundamentals, 420 inverse methods, 424–426 multicomponent-overloaded liquid chromatography, 426–428 peak deconvolution, 426–428 perturbation method, 423–424 Affinity chromatography, 20–25, see also Bioaffinity solid-phase sorbents; Immunoaffinity chromatography Agilent Eclipse XDB column, 301 Akzo Nobel company, 49 Albumin, 7, 33 Allergens, 16 Alprenolol, 397 Amino acids, affinity ligands, 14 2-aminophenol, 407 Ammonia, 395

Ammonium acetate, 397–398, 402 Ampholine, 27 Amylose tris(3,5-dimethylphenylcarbamate), 79–80 Analogies in ecology, 161–163 Aniline, 405 Anion exchange, 270–272 Anthraquinone dyes, 5 Antibodies high-abundance protein removal, 17, 19 interaction area, 6 isolation evaluation, 7 mixed-mode ligands, 6–7 selective ligand identification, 20 separation/purification, 5 Antifungal drugs, 117–119 Apolipoprotein A1, 38 Applications biological processes, 408–410 mixed bed media selection, 36 Applications, chromatographic separation and NMR CE isolates, 129 degradation products, 115–117 fundamentals, 115 impurities, 117–119 metabolites, 127–128 mixture analysis, 122–123 tautomer kinetics, 123, 125 trace analysis, 119–120, 122 unstable products, 125–127 Applications, hydrophobic-subtraction model column design, unique selectivity, 353–355 column manufacture control, 355–356 column selection, 349, 351–352 column selectivity, 347–349, 360–364 comparison, column selectivity, 347–349 degradation, stationary-phase, 356 description procedure comparison, column selectivity, 360–364 “de-wetting,” stationary-phase, 360 different selectivity, column selection, 351–352 function of columns, retention prediction, 356–358 fundamentals, 346 identification, column types, 356 number of columns, 362 peak tailing, anticipating, 352–353 retention predictions, 356–358, 364 similar selectivity, column selection, 349

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442 “slow” column equilibrium, 358–360 solute-column interaction measurements, 363–364 stationary-phase, 356, 360 stationary-phase composition, column selectivity, 364 summary, 364 types of columns, 356, 362–363 unique selectivity, column design, 353–355 Applications, nonlinear reversed phase liquid chromatography chiral liquid chromatography, 430–435 fundamentals, 428–429 hydrophobic and hydrophilic interation elution mechanisms, 435–438 mobile phase pH influence, 429–430 nonlinear behavior, 435–438 Aptamers, 5, 20 Aromatic rings, ligands, 7 Ascentis Express columns, 293, 328 ASMBC (amylose tris((S)-α-methylbenzylcarbamate)) dry PS sorbents, 63, 66 enantioselectivities, 74 fundamentals, 50 literature studies, 84 PPA with three sorbents, 75–76, 79 Astrocytic protein S100B, 15 Asymmetric peak pattern, 144 ATR, see Attenuated total reflection (ATR) Attenuated total reflection (ATR), 57, 63 Automated multidimensional chromatography, 122–123 Azoic dyes, 5

B Bead decoding, 25 Bead-plot method, 24 Bending vibration, 57 Benzimidazole, 398 Benzoic acid, 404–405 Berberine, 325, 327, 329 bi-Gaussian properties, 160, 162–163, see also Gaussian peak Bioaffinity solid-phase sorbents, 2, see also Affinity chromatography Biological processes applications, 408–410 Biomarker discovery, 38 “Blind” protein purification process, 28–31 Blood serum, 16 Blumberg comparison, 209–213 Boltzmann distribution, 95, 96 Bovine β-lactoglobulin, 7 Boxcar-type accumulator, 148 Brain-derived polypeptides, 15 Brain markers, 15

Index Brain pathologies, 15 Broadening factor, 186–187, 210 Buffer selection, 101–102 Buspirone, 123 Butylamine, 395

C CAD, see Cationic amphiphilic drugs (CADs) Calibration, 382, 394 Calixarenes, columns, 310 Camurri and Zaramella instrument, 385 Cancer antigen 125 (CA125), 38 Candida infections, 117 Capillary electrophoresis (CE) applications, 129 fundamentals, 112–113 isolation techniques, 112–113 Capillary isotachophoresis (cITP), 113 Capillary liquid chromatography, organic monolith column technology, see also Columns acronyms, 274–275 anion exchange, 270–272 capillary surface modification, 245–246 cation exchange, 268–269 column diameter, 244 column efficiency, 244 fundamentals, 238–239, 272–273 hydrophilic interaction, 264–266 hydrophobic interaction, 260–263 ion exchange, 267–272 monolith pore structure control and morphology, 249–254 monolith synthesis, 246–249 monomer ratio, 252–253 monomer to porogen ratio, 253–254 packed bed flow, 243–244 packed bed uniformity, 240–243 particle diameter, 244–245 particle morphology influence, 241–242 particle packed columns, 239–245 photoinitiated polymerization, 247–249 polymeric monolithic column technology, 245–254 polymeric monoliths for liquid chromatography, 254–272 porogens, 249–252 reversed phase, 254–260 size exclusive, 266–267 thermally initiated polymerization, 246–247 wall effects, 242–243 Capillary room temperature probes (CapNMR), 104–105 Carbamate-based chiral stationary phases, 430 Carboxylate-containing drugs, 125 Cardiovascular drugs, 48

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Index Casein, 15–16 Cation exchange capacity C-2.8, 332 capacity C-7.0, 331–332 fundamentals, 323–324 ion exchange, 268–269 peak tailing, 329–330 retention processes, 325–327 retention variation, 327–329 solute ionic charge κ, 330–331 stationary-phase charge, 324–325 values of C-2.8 < 0, 334–335 values of C-2.8 > 0, 332–333 Cationic amphiphilic drugs (CADs), 409–410 CD, see Circular dischroism (CD) spectroscopy CDA II hereditary disorder, 15 CDMPC (cellulose tris(3,5-dimethylphenylcarbamate)) ADMPC comparison, 79–80 dry PS sorbents, 63 enantioselectivities, 74 fundamentals, 50 PPA with three sorbents, 75–79 sorbent/solvent interactions, 72 CE, see Capillary electrophoresis (CE) Cell extracts, 16 Cellulose tris(3,5-dimethylphenylcarbamate), 79–80 Cerebrospinal fluid, see Human biologicals Challenges, chiral discrimination, 50, 53 Characteristic point, 421–423 Chelation, 19–20, 344, 363 Chemical shift, nuclear magnetic resonance theory, 98–99 CHI, see Chromatographic hydrophobicity index (CHI) Chiral cavity structures, 62–67 Chiralcel OD, 50 Chiral discrimination, polysaccharide phases acronyms, 86 amylose tris(3,5-dimethylphenylcarbamate), 79–80 cellulose tris(3,5-dimethylphenylcarbamate), 79–80 challenges, 50, 53 chiral cavity structures, 62–67 chromatography method, 55–56 circular dischroism spectroscopy, 56–59 cross polarization magic angle spinning, 61–62 dry polysaccharide sorbents, 62–67 effect on enantioselectivity, 74–84 fundamentals, 48–55, 85 future outlook, 85 homonuclear correlation spectroscopy, 60–61 importance, 48–50

443 infrared spectroscopy, 56–59 liquid state, 59–61 literature results, 80–82, 84 magic angle spinning, 61–62 mechanisms and methods summary, 84–85 methods used, 55–62 microstructures, 62–67 molecular simulations, 62 needs, 50, 53 norephedrine with three sorbents, 74–79 nuclear magnetic resonance spectroscopy, 59–62 nuclear Overhauser enhancement spectroscopy, 59–60 objectives, 50, 53 polysaccharide sorbent interactions, chiral solutes, 73–85 research strategies, 53–55 simple nonchiral solutes, 67–73 solid state, 61–62 solvents, 67–73 sorbent interactions, 67–73 symbols listing, 86 vibrational spectroscopies, 56–59 x-ray diffraction, 59 Chiral liquid chromatography, 430–435 Chiralpak AD, 50 Chiralpak AS, 50 Chiral stationary phases (CSPs) polysaccharide phases, chiral separations, 49 reversed phase conditions, 430–435 Chiral switching, 48 Chromatographic hydrophobicity index (CHI) biological processes applications, 408–410 experimental determination, 381–385 fundamentals, 377–385, 410 HPLC determination, lipophilicity, 378–379 hydrophobicity parameter comparisons, 389–393 ionizable compounds, 393–408 isocratic HPLC retention, 387, 389 linear solvation energy relationships, 385–393 lipophilicity, 379–380 monoprotic neutral compounds, 395–405 pH relationships, 393–408 polyprotic compounds, 405–408 Chromatographic separation and NMR applications, 115–129 capillary electrophoresis-NMR coupling, 112–113 CE isolates, 129 chemical shift, 98–99 cryocapillary probes, 106 cryoflow probes, 105–106 cryogenically cooled probes, 105–106 degradation products, 115–117

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444 experiments, 113–115 fundamentals, 94, 130–132 impurities, 117–119 instrumentation, 100–102 isolation techniques, 106–113 loop collector, 108 metabolites, 127–128 method development, 100–102 mixture analysis, 122–123 nuclear resonance and relaxation, 96–98 nuclei magnetic properties, 94–96 probe technologies, 103–106 room temperature flow probe, 103–104 room temperature microcapillary flow probe, 104–105 solid phase extraction, 109–112 spin coupling, 99–100 stop flow, 107–108 tautomer kinetics, 123, 125 theory, 94–100 trace analysis, 119–120, 122 unstable products, 125–127 ChromatoTOF, 200 Cibacron blue, immobilized, 17 Circular dischroism (CD) spectroscopy, 56–59 cITP, see Capillary isotachophoresis (cITP) Classical inverse methods, 425–426 Coefficients chromatographic hydrophobicity index, 382 hydrophobicity parameter comparisons, 390–391 isocratic HPLC retention, 389 linear solvation energy relationships, 386–387 octanol-water partition, 312 Columns, see also Organic monolith column technology Abraham columns, 389 Agilent Eclipse XDB, 301 Ascentis Express, 293, 328 “best” selection, 357 calixarenes, 310 cyclodextrin-based, 389 diameter, 244 Discovery column, 301 efficiency, 244–245 hydrogen-bond acidity, 321–323 hydrophobic H, 312–314 Inertsil ODS-3 column, 324, 389 Kinetex, 293 Lázaro column, 389 Luna, 349 Miyake columns, 389 parallel, 192–193, 194 particle diameter, 244–245 polymer-based, 389 Poroshell, 286, 293

Index properties, 341 Spherisorb, 348 StableBond, 324, 327, 334 steric resistance, 316–318 Symmetry, 334–335, 349, 359 XTerra, 325, 348 Columns, selectivity, see also Reversed-phase column selectivity, hydrophobicsubtraction model dependence on properties, 368–369 parameter measurements, 366–368 routine measurements, 307, 309–310 separation conditions effect, 306–307 similar, column selection, 349 stationary-phase composition, 364 unique, column design, 353–355 Combinatorial libraries mixed beds, selective ligand identification, 20–22 polishing aspect, 32 streamlining single-bed and mixed-bed chromatography, 37 Comparisons, one-dimensional-LC and LC × LC Blumberg comparison, 209–213 fundamentals, 206–207 Huang comparison, 213–216 observed or resolved peaks, numbers of, 217 peak capacity, 208–209 separation performance metrics, 207–217 Stoll comparison, 213–216 Comprehensive online multidimensional liquid chromatography analogies in ecology, 161–163 bilinear methods, 204–205 Blumberg comparison, 209–213 chemometric methods, 200–205 current metrics assessment, 165 derivation Guiochon's key equations, 217–218 ecology, 161–163 Fisher ratio analysis, 205–206 fundamentals, 140–144, 195, 217–218 future directions, 217–218 Gilar method reexamination, 163–165 glossary, 219–222 Guiochon group study, 179–186 Guiochon's key equations, derivation, 217–218 Horie theory study, 173–175 Huang comparison, 213–216 isocratic and gradient peak capacity comparison, 167–169 isocratic elution chromatograhy optimization, 169–173 LC × LC peak capacity, undersampling effect, 150

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Index Li theory study, 175–179 metabolomics, 205 models, 153–157 multilinear methods, 200–204 multiple parallel second-dimension columns, 192–193 nomenclature, 143–144 observed or resolved peaks, numbers of, 217 one-dimensional-LC and LC × LC comparison, 206–217 optimization, online LC × LC, 165–194 orthogonality, 153–157 peak-broadening factor models, 145, 147–150 peak capacity, 208–209 peak intensity, 195–200 practical peak capacity and fractional coverage, 158–165 principal component analysis, 206 quantification, 195–206 retention alignment methods, 205 separation performance metrics, 207–217 Shoenmakers studies, 173, 186–192 SOT-based determinations of , 150–153 Stoll comparison, 213–216 studies about, 173–194 summary, 194 two-dimensional peak capacity, 161 two-dimensional separation applications, 157–158 undersampling, first dimension, 144–153 Concomitant separation, mixed beds, 18–20 Connective tissue activating peptide III (CTAP3), 38 Continuous flow LC-NMR, 107 Convex hull peels method, 162 Cooperation, proteins, 13 Corn-seed extract, 161 Corrected two-dimensional peak capacity, 144, 178 Correlation optimized warping (COW), 205 COSY, see Homonuclear correlation spectroscopy (COSY) “Cotton effect,” 58 Couplets, 58–59 COW, see Correlation optimized warping (COW) CPMAS, see Cross polarization magic angle spinning (CPMAS) Craig algorithm, 419 Cross polarization magic angle spinning (CPMAS) dry PS sorbents, 65–67 enantioselectivities, 85 literature studies, 81 nuclear magnetic resonance spectroscopy, 61–62 Cryocapillary probes, 106, 122

Cryoflow probes, 105–106, 127 Cryogenically cooled probes, 105–106, 122 CSPs, see Chiral stationary phases (CSPs) CTAP3, see Connective tissue activating peptide III (CTAP3) Cucurbitacins, 408–409 Current metrics assessment, 165 Cyano column type, 310 Cyclodextrin-based columns, 389 Cyclodextrin-based sorbents, 53

D Daicel company, 49 Davis method and equation, 175, 218 Degradation products, 115–117 Dehydrogenases, 5 Density functional theory (DTF) simulations CDMPC/ADMPC comparison, 79 enantioselectivities, 74 literature studies, 84 molecular simulations, 62 PPA with three sorbents, 75, 77 solid state NMR, 61 sorbent/solvent interactions, 68, 72 vibrational spectroscopies, 58–59 Depletion methods, 17–18 Depression treatment, 48 Derivatized amylose or cellulose PS polymers, 49, 50 Deuterated solvents, 110–111, 127 Developments, see Historical developments Dextromethorphan, 402, 405 DFT, see Density functional theory (DTF) simulations Dibenzepinones, 408 Differential mass balance equations, 417, 418 Diffuse reflectance infrared (DR-IR) mode, 56 DIM, see Direct inverse methods (DIM) Diode array detector (DAD), 106, 203, 204, 218 Diphenhydramine, 397 Dirac impulse train, 148 Direct inverse methods (DIM), 424, 426 Discovery column, 301 Distribution, see ADMET behavior DNA GyraseB inhibitors, 385 Donnan effect, enhanced, 19 DotMap algorithm, 206 Downstream processing, 48 DR-IR, see Diffuse reflectance infrared (DR-IR) mode Dry polysaccharide sorbents, 62–67 Dual-color bead approaches, 23–24 Dye ligands, 4–5, 17 Dynamic concentration range, reduction, 12

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446 E Ecology, 161–163 Edman degradation, 25 Effective two-dimensional peak capacity, 143 Eggs, white and yolk, 16 Elastases, 5 Electron microscopy (EM), 409 Electro-osmotic flow (EOF), 129 Electrospray ionization (ESI), 102, 127 Elution by characteristic point, 422–423 mixed beds, 2 EM, see Electron microscopy (EM) Enantioresolution, 48–49 Enantioselectivity, 56, 74–84 End-capping, see Hydrophobic-subtraction model Energy of a nucleus, 95 Enhanced Donnan effect, 19 Enhancement, very low abundance proteins, 10–16 Enolase, neuron-specific, 15 Enzyme-linked colorimetric assay, 24 EOF, see Electro-osmotic flow (EOF) Ephedrine, 398, 402, 405 Eppendorf tube, 120, 122 Equilibrium-dispersive model, 418–419 Equipment costs, 49 Errors column cation-exchange, 332 column selectivity comparison, 347 optimization, 181 peak deconvolution, 427 solute-column interactions, hydrophobicsubtraction model, 344–346 Escherichia coli, 27, 33 ESI, see Electrospray ionization (ESI) Euclidean distance, 155 Euerby procedure, 361–363 Excretion, see ADMET behavior Experiments chromatographic hydrophobicity index, 381–385 chromatographic separation and NMR, 113–115 Exponentially modified Gaussian peak model, 198

F Fast liquid chromatography, 170 Fisher ratio analysis, 205 Flow probe, LC-NMR system, 101 Flow-sheeting tools, 32 Fourier transform, 58 Fractal scaling law, 156

Index Fractional coverage and practical peak capacity analogies in ecology, 161–163 current metrics assessment, 165 ecology, 161–163 fundamentals, 158–161 Gilar method reexamination, 163–165 peak capacity, 208 two-dimensional peack capacity, 161 Fractionation glycoproteins, 18–19 isoelectric group separation, 25, 27 mixed beds, 3 Fraction collector, 108 Frontal analysis (FA) method, 420–421 Frontal analysis by characteristic point (FACP) method, 421–422 “Frustrated” electromagnetic waves, 57 Functional group analysis, 54–55 Functionals, 62 Fusion proteins, 22 Future directions chiral discrimination, polysaccharide phases, 85 multidimensional liquid chromatography, 217–218 superficially porous particles, 293

G GAGs, see Glycosaminoglycans (GAGs) Gastrointestinal drugs, 48 Gaussian peak, 144, 145, 147, see also bi-Gaussian properties GC Image software, 200 Generalized rank annihilation (GRAM), 203 General rate model (GRM), 419–420 Gidding’s sample dimensionality, 154, 156 Gilar method reexamination, 163–165 Glossary, multidimensional liquid chromatography, 219–222 Glueckauf method, 434 Glycoproteins, 5 Glycosaminoglycans (GAGs), 129 Glyomas, 15 Gradient peak and isocratic capacity comparison, 167–169, 187 GRAM, see Generalized rank annihilation (GRAM) Grignard dimerization, 258 GRM, see General rate model (GRM) Guiochon group study, 179–186 Guiochon’s key equations, derivation, 217–218

H HALO, 290–291 Harmonic means method, 162

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Index Helmholtz coil design, 129 Hepcidin, 38 Heterocyclic molecules and compounds, 5, 7 Heteronuclear multiple quantum correlation spectroscopy, see HMQCS Heteronuclear single quantum correlation spectroscopy (HSQCS), see HSQCS Hexapeptide libraries, 12 HICRAM, 119–120 High-abundance proteins mixed beds, 11 removal, mixed beds, 17–18 High performance/pressure liquid chromatography (HPLC) “blind” protein purification process, 30 lipophilicity, 378–379 High-resolution flow probes, 103–104 Historical developments hydrophobic-subtraction model, 301–306 superficially porous particles, 281–292 HMQCS (heteronuclear multiple quantum correlation spectroscopy), 114–115 “Home range,” 161 Homonuclear correlation spectroscopy (COSY) impurities, 117, 119 liquid state NMR, 60–61 NMR experiments, 114 Horie theory study, 173–175, 176, 182 HPLC, see High performance/pressure liquid chromatography (HPLC) HSQCS (heteronuclear single quantum correlation spectroscopy), 114–115 Huang comparison, 215–216 Human biologicals high-abundance protein removal, 17 mixed-bed peptide libraries, 15 mixed-mode lectin column, 4 paracetamol, 127 Human factor IX, 23 Hydrocarbon alkyl chains, 7 Hydrogen bonding B as function of column properties, 341 CDMPC/ADMPC comparison, 79–80 column hydrogen-bond acidity, 321–323 dry PS sorbents, 63 fundamentals, 335 hydrogen-bond basicity origins, 341–343 hydrogen-bond basicity vs. hydrophobicity, 338, 340–341 literature studies, 80, 82 research strategies, 53 solute hydrogen-bond acidity, 335–338 solute hydrogen-bond basicity, 319–320 type-B alkylsilica columns, 341 very low abundance protein enhancement, 12 vibrations, 57

447 Hydrophilic interactions nonlinear reversed phase liquid chromatography, 435–438 polymeric monoliths for liquid chromatography, 264–266 Hydrophobic charge induction chromatography, 6 Hydrophobic interactions elution, 5 hydrophobic-subtraction model, 312–314 nonlinear reversed phase liquid chromatography, 435–438 polymeric monoliths for liquid chromatography, 260–263 Hydrophobicity parameter comparisons, 389–393 Hydrophobic-subtraction model, reversed-phase column selectivity additional interactions, 343–344 applications, 346–360 B as function of column properties, 341 cation exchange κ′C, 323–335 column cation-exchange capacities, 331–332 column design, unique selectivity, 353–355 column hydrogen-bond acidity, 321–323 column hydrophobic H, 312–314 column manufacture control, 355–356 column selection, 349, 351–352 column steric resistance, 316–318 comparison, column selectivity, 347–349 cyano column type, 310 degradation, stationary-phase, 356 description procedure comparison, 360–364 development, 301–306 “de-wetting,” stationary-phase, 360 different selectivity, column selection, 351–352 error in model, 344–346 function of columns, retention prediction, 356–358 fundamentals, 299–300, 365–366 hydrogen-bond basicity, 338, 340–343 hydrogen bonding, 319–323, 335–343 hydrophobic interaction, 312–314 hydrophobicity H comparison, 338, 340–341 identification, column types, 356 measurements, 307, 309–310, 363–364 modeling, 300–310 number of columns, 362 peak tailing, 329–330, 352–353 phenyl column type, 310 properties, selectivity dependence on, 368–369 retention predictions, 356–358, 364 retention processes, 325–327 retention variation, 327–329

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448 routine measurement of column selectivity, 307, 309–310 selectivity dependence on properties, 368–369 separation conditions effect, column selectivity, 306–307 similar selectivity, column selection, 349 “slow” column equilibrium, 358–360 solute bulkiness, 315–316 solute-column interactions, 310–346, 363–364 solute hydrogen-bond acidity, 335–338 solute hydrogen-bond basicity, 319–320 solute hydrophobic interactions, 312 solute ionic charge κ′, 330–331 stationary-phase, 324–325, 356, 360, 364 steric interactions, 314–319 summary, 364 symbols, 371–372 type-B alkylsilica columns, 341 types of columns, 356, 362–363 unique selectivity, column design, 353–355 values of C-2.8 < 0, 334–335 values of C-2.8 > 0, 332–333

I Ibuprofen, 404–405 Icofungipen, 117–119 Ideal model, 417–418 IgG antibodies, 5, 7 IKSFA, see Iterative key set factor analysis (IKSFA) Image analysis software, 199 Image subtraction approach, 24 Imipramine, 398, 402 Immobilized Cibacron blue, 17 Immunoaffinity chromatography, see also Affinity chromatography; Bioaffinity solid-phase sorbents immobilized antibodies, 8 mixed mode, 3–4 Impurities chromatographic separation and NMR applications, 117–119 removal, 32–35 streamlining single-bed and mixed-bed chromatography, 36 Inertsil ODS-3 columns, 324, 327 Information entropy of Shannon, 154 Infrared (IR) spectroscopy CDMPC/ADMPC comparison, 79 enantioselectivities, 74, 85 fundamentals, 56–59 literature studies, 81–82 sorbent/solvent interactions, 72 Inphase properties, 144, 196

Index Instrumentation, LC-NMR, 100–102 Inter-a-trypsin inhibitor heavy chain 4 (ITIH4), 38 Interlaboratory reproducibility of values, 309 Inverse methods, 424–426 Inverted watershed algorithm, 199 Ion exchange and exchangers anion exchange, 270–272 cation exchange, 268–269 fundamentals, 267–268 mixed beds, 2 Ion exchange chromatography, 7 Ionic interactions, elution, 5 Ionizable compounds monoprotic neutral compounds, 395–405 pH relationship with CHI, 393–395 polyprotic compounds, 405–408 Ionized silanols, 324, 333, 366 IR, see Infrared (IR) spectroscopy Isocratic and gradient peak capacity comparison, 167–169, 187 Isocratic elution chromatograhy optimization, 169–173 Isocratic HPLC retention, 387, 389 Isoelectric group separation, 25–27 Isolation techniques, chromatographic separation and NMR capillary electrophoresis-NMR coupling, 112–113 fundamentals, 106–107 loop collector, 108 solid phase extraction, 109–112 stop flow, 107–108 Iterative key set factor analysis (IKSFA), 204 ITIH4, see Inter-a-trypsin inhibitor heavy chain 4 (ITIH4)

J J-coupling, 99

K Katholieke Universiteit Leuven (KUL), 361, 363 Kernels method, 162 Ketoenol tautomerization, 123 Kinases, 5 Kinetex columns, 293 Kinetics, 12, see also Mass transfer kinetics Knockout mouse approach, 55, 79 Knox equation, 170 Kozeny-Carman equation, 170

L Langmuir-Moreau model, 435 Langmuir-type properties

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449

Index frontal analysis by characteristic point, 422 ideal model, 417 mobile phase pH, 430 perturbation method, 423 reversed phase conditions, 432 Larmor precessional frequency, 97–98 Latex, 16 Lázaro column, 389 LC × LC, one-dimensional-LC comparison Blumberg comparison, 209–213 fundamentals, 206–207 Huang comparison, 213–216 observed or resolved peaks, numbers of, 217 peak capacity, 208–209 separation performance metrics, 207–217 Stoll comparison, 213–216 LC × LC, online optimization fundamentals, 166–167 Guiochon group study, 179–186 Horie theory study, 173–175 isocratic and gradient peak capacity comparison, 167–169 isocratic elution chromatograhy optimization, 169–173 Li theory study, 175–179 multiple parallel second-dimension columns, 192–193 Shoenmakers studies, 173, 186–192 studies about, 173–194 summary, 194 LC-MS/MS, see Liquid chromatography-tandem mass spectrometry (LC-MS/MS) LE, see Leading electrolyte (LE) Leading electrolyte (LE), 129 Least squares appproach, 162 Lectins, concomitant separation, 18–19 L-enantiomers, 80–81, 84 Libraries combinatorial, 20–22, 32, 37 mixed-bed peptides, 10–16 mixed ligands, 34, 36 one-bead-one-ligand, 20–21 small-molecule combinatorial, 24 solid-phase mixed-bed ligands, 22 solid-phase peptides, 14 tripeptides, 14 Lidocaine, 398 Ligand concentration, see Hydrophobicsubtraction model Ligand length, see Hydrophobic-subtraction model Ligands identification, affinity chromatography, 20–25 mixed beds, 9 polishing aspect, 34 Limulus polyphemus hemolymph, 16

Linear free energy relationships (LFERs) fundamentals, 385–387 hydrophobic-substraction model, 302 Linear solvation energy relationships (LSERs) fundamentals, 385–387 hydrophobicity parameter comparisons, 389–393 isocratic HPLC retention, 387, 389 Lipitor, 48 Lipophilicity descriptor, 379–380 HPLC determination, 378–379 index, 380 Liquid chromatography-tandem mass spectrometry (LC-MS/MS) high-abundance protein removal, 18, 19 Liquid state nuclear magnetic resonance spectroscopy, 59–61 Literature results, 80–82, 84 Li theory study, 175–179, 182–183 Local convex hulls method, 162 Loop collector, 108 Low abundance proteins, 10–16 LSER, see Linear solvation energy relationships (LSERs) Luna columns, 349

M Magic angle spinning (MAS) dry PS sorbents, 66–67 enantioselectivities, 85 nuclear magnetic resonance spectroscopy, 61–62 PPA with three sorbents, 76 Magnetic quantum number, 96 Magnetogyric ratio, 95 Martin-Synge algorithm, 419 Mass spectrometry (MS), 30 Mass-tag encoding strategy, 24 Mass transfer kinetics, 418, see also Kinetics Maximum achievable corrected peak capacity, 184 Maximum flow cell performance, 103 MCR, see Multivariate curve resolution (MCR) MD, see Molecular dynamics (MD) method Measurements column selectivity, 307, 309–310 column-selectivity, 366–368 solute-column interactions, 363–364 Mechanisms, polysaccharide sorbent interactions, 84–85 Media selection, 35–36 MEph (methyl ephedrine) CDMPC/ADMPC, 79–80 molecular structures, 50 Metabolism, see ADMET behavior

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450 Metabolites, 127–128 Methanol, 398, 402, 405 Methods chiral discrimination, polysaccharide phases, 55–62 LC-NMR, 100–102 polysaccharide sorbent interactions, chiral solutes, 84–85 Metoprolol, 397 Metrics, assessment, 165 Microcoil NMR spectroscopy, 112 Microcryotechnology, 106 Microglobulin, 38 Microstructures, dry polysaccharide sorbents, 62–67 Minimum convex polygon method, 162 “Ministorage column,” 110 Mixed beds “blind” protein purification process, 28–31 concomitant separation, 18–20 enhancement, very low abundance proteins, 10–16 fundamentals, 1–4, 37–38 high-abundance proteins, removal, 17–18 impurities removal, 32–35 isoelectric group separation, 25–27 ligand identification, affinity chromatography, 20–25 media selection, 35–36 mixed-mode interactions, 4–10 mixed-mode sorbents, 9 polishing aspects, 32–35 removal, high-abundance proteins, 17–18 scheme applications, 31–37 separation, protein categories, 16–20 single-mode sorbents, 9 single molecular interactions, 4–10 streamlining single-bed with mixed-bed, 36–37 very low abundance proteins, enhancement, 10–16 Mixed ligands libraries polishing aspect, 34 streamlining single-bed and mixed-bed chromatography, 36 Mixed-mode interactions, 4–10 Mixed-mode ligands classification, 4–5 Mixture analysis, 122–123 Miyake columns, 389 M-LAC, 19 Mobile phase pH influence multicomponent-overloaded liquid chromatography, 429–430 nonlinear reversed phase liquid chromatography, 429–430 Modeling, hydrophobic-subtraction cyano column type, 310

Index development, 301–306 fundamentals, 300–301 phenyl column type, 310 routine measurement, column selectivity, 307, 309–310 separation conditions effect, column selectivity, 306–307 Models equilibrium-dispersive model, 418–419 exponentially modified Gaussian peak model, 198 general rate model, 419–420 ideal model, 417–418 nonlinear reversed phase liquid chromatography, 416–420 orthogonality, 153–157 Molecular dynamics (MD) method CDMPC/ADMPC comparison, 79 fundamentals, 62 literature studies, 80, 84 PPA with three sorbents, 75–79 PS sorbents/chiral solutes interactions, 74 Molecular simulations, 62 Monolith pore structure control and morphology fundamentals, 249 monomer ratio, 252–253 monomer to porogen ratio, 253–254 porogens, 249–252 Monolith synthesis fundamentals, 246 photoinitiated polymerization, 247–249 thermally initiated polymerization, 246–247 Monomer ratio, 252–253 Monomer to porogen ratio, 253–254 Monoprotic neutral compounds, 395–405 Monte Carlo simulations, 149, 162 Multicomponent-overloaded liquid chromatography adsorption isotherms, 426–428 fundamentals, 428–429 mobile phase pH influence, 429–430 Multidimensional liquid chromatography, see Online comprehensive multidimensional liquid chromatography Multiple parallel second-dimension columns, 192–193 Multiple trapping, 110 Multivariate curve resolution (MCR), 195, 204 Murphy sampling rate, 173–174, 176–177 Mutarotation, 125–127

N 2-naphthol, 398, 402 Naproxen enantiomers, 432 Nearest-neighbor clusters method, 162

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451

Index Nearest-neighbor convex hulls method, 162 Needs, chiral discrimination, 50, 53 Neuron-specific enolase, 15 Neurophilin-1 and 2, 15 Nicotine, 395, 398 Nile red, 409 NMR, see Nuclear magnetic resonance (NMR) NOESY, see Nuclear Overhauser enhancement spectroscopy (NOESY) Nomenclature, multidimensional liquid chromatography, 143–144 Nonlinear behavior, 435–438 Nonlinear reversed phase liquid chromatography adsorption isotherms, 420–428 applications, 426–438 characteristic point, 421–423 chiral liquid chromatography, 430–435 classical inverse methods, 425–426 direct inverse methods, 426 elution, 422–423 equilibrium-dispersive model, 418–419 frontal analysis, 420–422 fundamentals, 416 general rate model, 419–420 hydrophobic and hydrophilic interation elution mechanisms, 435–438 ideal model, 417–418 inverse methods, 424–426 mobile phase pH influence, 429–430 models, 416–420 multicomponent-overloaded liquid chromatography, 426–428 nonlinear behavior, 435–438 peak deconvolution, 426–428 perturbation method, 423–424 Nonzwittertonic properties, polyprotic compounds, 407 Norephedrine, 50, 74–79 Norfloxacin, 407 Nortiptyline, 398, 402 Nuclear magnetic resonance (NMR), chromatographic separation applications, 115–129 capillary electrophoresis-NMR coupling, 112–113 CE isolates, 129 chemical shift, 98–99 cryocapillary probes, 106 cryoflow probes, 105–106 cryogenically cooled probes, 105–106 degradation products, 115–117 experiments, 113–115 fundamentals, 94, 130–132 impurities, 117–119 instrumentation, 100–102 isolation techniques, 106–113 loop collector, 108

metabolites, 127–128 method development, 100–102 mixture analysis, 122–123 nuclear resonance and relaxation, 96–98 nuclei magnetic properties, 94–96 probe technologies, 103–106 room temperature flow probe, 103–104 room temperature microcapillary flow probe, 104–105 solid phase extraction, 109–112 spin coupling, 99–100 stop flow, 107–108 tautomer kinetics, 123, 125 theory, 94–100 trace analysis, 119–120, 122 unstable products, 125–127 Nuclear magnetic resonance (NMR) spectroscopy cross polarization magic angle spinning, 61–62 homonuclear correlation spectroscopy, 60–61 liquid state, 59–61 magic angle spinning, 61–62 molecular simulations, 62 nuclear Overhauser enhancement spectroscopy, 59–60 solid state, 61–62 Nuclear Overhauser enhancement spectroscopy (NOESY) dry PS sorbents, 63, 65 liquid state NMR, 59–60 literature studies, 80, 84 NMR experiements, 114 Nuclear shielding, 98–99 Nuclei magnetic properties, 94–96 Nyquist theorem, 140

O Objectives, 50, 53 Observed or resolved peaks, numbers of, 217 OCFE, see Orthogonal collocation on finite elements (OCFE) Octanol-water partition coefficient, 312 Oligonucleotides, 5 One-bead-one-ligand libraries, 20–21 One-dimensional-LC and LC × LC comparison Blumberg comparison, 209–213 fundamentals, 206–207 Huang comparison, 213–216 observed or resolved peaks, numbers of, 217 peak capacity, 208–209 separation performance metrics, 207–217 Stoll comparison, 213–216 Online comprehensive multidimensional liquid chromatography

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452 analogies in ecology, 161–163 bilinear methods, 204–205 Blumberg comparison, 209–213 chemometric methods, 200–205 current metrics assessment, 165 derivation Guiochon's key equations, 217–218 ecology, 161–163 Fisher ratio analysis, 205–206 fundamentals, 140–144, 195, 217–218 future directions, 217–218 Gilar method reexamination, 163–165 glossary, 219–222 Guiochon group study, 179–186 Guiochon's key equations, derivation, 217–218 Horie theory study, 173–175 Huang comparison, 213–216 isocratic and gradient peak capacity comparison, 167–169 isocratic elution chromatograhy optimization, 169–173 LC × LC peak capacity, undersampling effect, 150 Li theory study, 175–179 metabolomics, 205 models, 153–157 multilinear methods, 200–204 multiple parallel second-dimension columns, 192–193 nomenclature, 143–144 observed or resolved peaks, numbers of, 217 one-dimensional-LC and LC × LC comparison, 206–217 optimization, online LC × LC, 165–194 orthogonality, 153–157 peak-broadening factor models, 145, 147–150 peak capacity, 208–209 peak intensity, 195–200 practical peak capacity and fractional coverage, 158–165 principal component analysis, 206 quantification, 195–206 retention alignment methods, 205 separation performance metrics, 207–217 Shoenmakers studies, 173, 186–192 SOT-based determinations, 150–153 Stoll comparison, 213–216 studies about, 173–194 summary, 194 two-dimensional peak capacity, 161 two-dimensional separation applications, 157–158 undersampling, first dimension, 144–153 Online sample preparation system, 122–123 Optimization, online LC × LC fundamentals, 166–167

Index Guiochon group study, 179–186 Horie theory study, 173–175 isocratic and gradient peak capacity comparison, 167–169 isocratic elution chromatograhy optimization, 169–173 Li theory study, 175–179 multiple parallel second-dimension columns, 192–193 Shoenmakers studies, 173, 186–192 studies about, 173–194 summary, 194 Organic modifier fraction, 379 Organic monolith column technology, see also Columns acronyms, 274–275 anion exchange, 270–272 capillary surface modification, 245–246 cation exchange, 268–269 column diameter, 244 column efficiency, 244 fundamentals, 238–239, 272–273 hydrophilic interaction, 264–266 hydrophobic interaction, 260–263 ion exchange, 267–272 monolith pore structure control and morphology, 249–254 monolith synthesis, 246–249 monomer ratio, 252–253 monomer to porogen ratio, 253–254 packed bed flow, 243–244 packed bed uniformity, 240–243 particle diameter, 244–245 particle morphology influence, 241–242 particle packed columns, 239–245 photoinitiated polymerization, 247–249 polymeric monolithic column technology, 245–254 polymeric monoliths for liquid chromatography, 254–272 porogens, 249–252 reversed phase, 254–260 size exclusive, 266–267 wall effects, 242–243 Orthogonal collocation on finite elements (OCFE), 419 Orthogonality agreement, lacking, 153 analogies in ecology, 161–163 current metrics assessment, 165 ecology, 161–163 fundamentals, 153 geometric, 154–155 Gilar method reexamination, 163–165 models, 153–157 multidimensional liquid chromatography, 141

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Index practical peak capacity and fractional coverage, 158–165 streamlining single-bed and mixed-bed chromatography, 36 two-dimensional peak capacity, 161 two-dimensional separation applications, 157–158 Out of phase properties, 144, 196 OVA1, 38 Ovarian cancer, 38 Overactive bladder treatment, 116 Overloading conditions polishing aspect, 32 very low abundance protein enhancement, 12, 14 Oxprenolol, 397

P Packed bed flow particle packed columns, 243–244 Packed bed uniformity fundamentals, 240–241 particle morphology influence, 241–242 wall effects, 242–243 Paracetamol, 127 PARAFAC, see Parallel factor analysis (PARAFAC) Parallel columns, 192–193, 194 Parallel factor analysis (PARAFAC), 195, 203, 205, 218 Pareto method, 149, 189–190 Parkinson disease-associated proteins, 15 Particle diameter, 244–245 Particle morphology influence, 241–242 Particle packed columns column diameter, 244 column efficiency, 244 fundamentals, 239–240 packed bed flow, 243–244 packed bed uniformity, 240–243 particle diameter, 244–245 particle morphology influence, 241–242 wall effects, 242–243 Pascal’s triangle, 100 PCA, see Principal component analysis (PCA) Peak capacity corrected two-dimensional peak capacity, 144, 178 effective two-dimensional, 143 limitations, 186 maximum achievable corrected peak capacity, 184 multidimensional liquid chromatography, 142 separation performance metrics, 208–209 Peak deconvolution, 426–428

453 Peak tailing cation exchange, hydrophobic-subtraction model, 329–330 mobile phase concentrations, 429 sorbent particles, 56 Peptides libraries, 10–16 mixed beds, selective ligand identification, 20 mixed-mode chromatography, 8 Permaphase, 285 Perturbation method, 423–424 Phase collapse, 360 Phenobarbital, 398, 402 Phenylalanine, 407 Phenyl column type, 310 Phosphate buffers, 101–102 Phosphorpeptides, 19 Phosphorproteins, 19 Phosphorylation, 19 Photoinitiated polymerization, 247–249 pH values chromatographic hydrophobicity index, 380, 383, 393–395 isoelectric group separation, 25–26 milk whey, 7 monoprotic neutral compounds, 395–405 polyprotic compounds, 405–408 reversed phase conditions, 432–435 very low abundance protein enhancement, 12 Pichia pastoris, 33 ∏-π interactions CDMPC/ADMPC comparison, 79–80 hydrophobic-subtraction model, 319 literature studies, 82 solute-column interactions, 343 PIQ, see Preferential interaction quadratic (PIQ) model Pirkle-type chiral stationary phases, 430–435 Planck’s constant, 95 Plant extracts, 16 Polishing aspects, 32–35 Polymer-based columns, 389 Polymeric monolithic column technology capillary surface modification, 245–246 monolith pore structure control and morphology, 249–254 monolith synthesis, 246–249 monomer ratio, 252–253 monomer to porogen ratio, 253–254 photoinitiated polymerization, 247–249 porogens, 249–252 thermally initiated polymerization, 246–247 Polymeric monoliths for liquid chromatography anion exchange, 270–272 cation exchange, 268–269

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454 fundamentals, 267–268 hydrophilic interaction, 264–266 hydrophobic interaction, 260–263 ion exchange, 267–272 reversed phase, 254–260 size exclusive, 266–267 Polypeptides, brain-derived, 15 Polyprotic compounds, 405–408 Polysaccharide sorbent interactions, chiral solutes amylose tris(3,5-dimethylphenylcarbamate), 79–80 cellulose tris(3,5-dimethylphenylcarbamate), 79–80 effect on enantioselectivity, 74–84 fundamentals, 73–74 literature results, 80–82, 84 mechanisms and methods summary, 84–85 norephedrine with three sorbents, 74–79 Poppe plot and approach, 170–171, 173–174, 182 Pore diameter, see Hydrophobic-subtraction model Porogens, 249–252 Poroshell columns, 286, 293 Positive beads, 23 Postacquisition coaddition, spectra, 129 PPA (norephedrine) molecular structure, 50 three sorbents results, 74–79 Practical peak capacity and fractional coverage analogies in ecology, 161–163 current metrics assessment, 165 ecology, 161–163 fundamentals, 158–161 Gilar method reexamination, 163–165 two-dimensional peack capacity, 161 Preferential interaction quadratic (PIQ) model, 436 Pressurized loops, 108 Principal component analysis (PCA), 206 Prion proteins, 22 Probe technologies cryocapillary probes, 106 cryoflow probes, 105–106 cryogenically cooled probes, 105–106 fundamentals, 103 room temperature flow probe, 103–104 room temperature microcapillary flow probe, 104–105 Procaine, 395, 398 Product rule, 141 Properties, column selectivity dependence, 368–369 Propranolol, 123, 397 Proteins capturing, 12 enhancement of very low, 10–16

Index Protein separation concomitant separation, similar molecular interactions, 18–20 fundamentals, 16–17 place of mixed-mode chromatography, 31–37 removal, high-abundance proteins, 17–18 ProteoMiner treatment, 15–16 Prozac, 48 Purification, see “Blind” protein purification process Pyridine, 402, 405 Pyrilamine, 397

Q Quantitative structure enantioselective retention relationships (QSERRs), 53 Quantum dot/COPAS assay, 24

R Racemates, 48 Radial heterogeneity, 242, 246 Radiation absorption, 98 Recombinant albumin, 33, see also Albumin Reequilibrium time, 169, 176 Regeneration conditions, 35 Relaxation, nuclear magnetic resonance theory, 96–98 Removal, high-abundance proteins, 17–18 Research strategies, 53–55 Resolved or observed peaks, numbers of, 217 Respiratory diseases, 48 Retention chromatographic hydrophobicity index, 383 predictions, 356–358 processes, 325–327 processes, cation exchange, 325–327 solid phase extraction system, 111 sorbent/solvent interactions, 71–72 variation, 327–329 variation, cation exchange, 327–329 Reversed phase, polymeric monoliths, 254–260 Reversed-phase column selectivity, hydrophobic-subtraction model additional interactions, 343–344 applications, 346–360 B as function of column properties, 341 cation exchange κ′C, 323–335 column cation-exchange capacities, 331–332 column design, unique selectivity, 353–355 column hydrogen-bond acidity, 321–323 column hydrophobic H, 312–314 column manufacture control, 355–356 column selection, 349, 351–352 column steric resistance, 316–318 comparison, column selectivity, 347–349

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Index cyano column type, 310 degradation, stationary-phase, 356 description procedure comparison, 360–364 development, 301–306 “de-wetting,” stationary-phase, 360 different selectivity, column selection, 351–352 error in model, 344–346 function of columns, retention prediction, 356–358 fundamentals, 299–300, 365–366 hydrogen-bond basicity, 338, 340–343 hydrogen bonding, 319–323, 335–343 hydrophobic interaction, 312–314 hydrophobicity H comparison, 338, 340–341 identification, column types, 356 measurements, 307, 309–310, 363–364 modeling, 300–310 number of columns, 362 peak tailing, 329–330, 352–353 phenyl column type, 310 retention predictions, 356–358, 364 retention processes, 325–327 retention variation, 327–329 routine measurement of column selectivity, 307, 309–310 separation conditions effect, column selectivity, 306–307 similar selectivity, column selection, 349 “slow” column equilibrium, 358–360 solute bulkiness, 315–316 solute-column interactions, 310–346, 363–364 solute hydrogen-bond acidity, 335–338 solute hydrogen-bond basicity, 319–320 solute hydrophobic interaction, 312 solute ionic charge κ′, 330–331 stationary-phase, 324–325, 356, 360, 364 steric interactions, 314–319 summary, 364 symbols, 371–372 type-B alkylsilica columns, 341 types of columns, 356, 362–363 unique selectivity, column design, 353–355 values of C-2.8 < 0, 334–335 values of C-2.8 > 0, 332–333 Reversed-phase high-performance liquid chromatography (RP-HPLC), 378 ROESY, see Rotating frame overhauser effect spectroscopy (ROESY) Room temperature flow probes, 103–104 Room temperature microcapillary flow probes, 104–105 Rotating frame overhauser effect spectroscopy (ROESY), 114 Rouchon algorithm, 419

Routine measurements, column selectivity, 307, 309–310, 366–368 RP-HPLC, see Reversed-phase highperformance liquid chromatography (RP-HPLC)

S Saddle coils, 112–113 Salicylic acid, 407 Saturation, 98 Scheme applications, mixed beds fundamentals, 31–32 impurities removal, 32–35 media selection, 35–36 polishing aspects, 32–35 streamlining single-bed with mixed-bed, 36–37 SDS-PAGE, see Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) SEC, see Size exclusion chromatography (SEC) Selected ion recording (SIR) chromatograms, 384 Semaphorin 3B, 15 Semipreparative chromatography, 122 Sensitivity issues capillary electrophoresis, 129 NMR spectroscopy, 116 trace analysis, 122 Separation concomitant separation, 18–20 conditions effect, column selectivity, 306–307 efficiency, 2–3 fundamentals, 16–17 protein categories, 16–20 removal, high-abundance proteins, 17–18 selectivity, 2–3 Separation, performance metrics Blumberg comparison, 209–213 fundamentals, 207 Huang comparison, 213–216 observed or resolved peaks, numbers of, 217 peak capacity, 208–209 Stoll comparison, 213–216 Separation dimensionality of Schure, 157 Shake flask method, 392 Shoenmakers studies, 173, 186–192 Signal-to-noise limitations, 107 Simple nonchiral solutes, 67–73 Simulated moving bed (SMB) processes, 48 Single-beds, streamlining with mixed-beds, 36–37 Single enantiomer drug development, 48 Singular value decomposition (SVD), 202, 204

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456 SIR, see Selected ion recording (SIR) chromatograms Size exclusion chromatography (SEC), 266–267, 314 Small-molecule combinatorial libraries, 24 Snake venom, 15 Snapshot sampler, 148 Sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) “blind” protein purification process, 30 mixed bed media selection, 36 very low abundance protein enhancement, 12, 16 Software column selectivity, 348 image analysis, 199 LC-NMR system, 101 peak intensity quantification, 200 Solenoid microcoils, 112–113 Solid phase extraction (SPE) cryocapillary probe, 106 fundamentals, 94 isolation techniques, 107, 109–112 LC-NMR system, 102 trace analysis, 119 Solid-phase mixed-bed ligands libraries, 22 Solid-phase peptide libraries, 14 Solid phase support, 2 Solid-state buffers, 25 Solid state nuclear magnetic resonance spectroscopy, 61–62, 85 Solute bulkiness, 315–316 Solute-column interactions, hydrophobicsubtraction model, 310–346 additional interactions, 343–344 B as function of column properties, 341 cation exchange κ′C, 323–335 column cation-exchange capacities, 331–332 column hydrogen-bond acidity A, 321–323 column hydrophobic H, 312–314 column steric resistance, 316–318 error in model, 344–346 fundamentals, 310–311 hydrogen-bond basicity, 338, 340–343 hydrogen bonding, 319–323, 335–343 hydrophobic interaction, 312–314 hydrophobicity H comparison, 338, 340–341 peak tailing, 329–330 retention processes, 325–327 retention variation, 327–329 solute bulkiness, 315–316 solute hydrogen-bond acidity, 335–338 solute hydrogen-bond basicity, 319–320 solute hydrophobic interaction, 312 solute ionic charge κ′, 330–331 stationary-phase charge, 324–325

Index steric interactions, 314–319 type-B alkylsilica columns, 341 values of C-2.8 < 0, 334–335 values of C-2.8 > 0, 332–333 Solute hydrogen-bond acidity, 335–338 Solute hydrogen-bond basicity, 319–320 Solute hydrophobic interaction, 312 Solvents, sorbent interactions, 67–73 Sorbents “blind” protein purification process, 28–31 costs, PS-based chiral, 50 cyclodextrin-based, 53 particle size, 56 simple nonchiral solutes, 67–73 solvents, 67–73 SOT, see Statistical-overlap theory (SOT) simulations Spark Prospect 2 SPE system, 127 SPE, see Solid phase extraction (SPE) Spectral counting, 19 Spherisorb columns, 325 Spin coupling, 99–100 SPPs, see Superficially porous particles (SPPs) StableBond columns, 324, 327, 334 Standing concentration waves, 49 Stationary-phase charge, 324–325 Statistical-overlap theory (SOT) simulations, 148–153, 160, 212 Stereospecific interactions, chiral selectivity, 50, 53 Steric hindrance, 79–80 Steric interactions column steric resistance, 316–318 fundamentals, 314–315 solute bulkiness, 315–316 Stokes diameter, 314 Stoll comparison, 213–214 Stop-and-go 2D-LC, 140 Stop flow system and analysis impurities, 117 isolation techniques, 107–108 ketoenol tautomerization, 123 unstable products, 125 Superconducting magnet, LC-NMR system, 101 Superficially porous particles (SPPs) future developments, 293 historical developments, 281–292 Surface grafting, 271 SVd, see Singular value decomposition (SVD) Symbols chiral discrimination, polysaccharide phases, 86 hydrophobic-subtraction model, 371–372 Symmetry columns, 334–335, 349, 359 Synthetic structures, 20

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Index T

V

Tanaka group, 173, 192 Tautomer kinetics, 123, 125 TCI MicroCryo Probe, 106 TE, see Trailing electrolyte (LE) TEA, see Triethylamine (TEA) Terbutaline, 395 4-tert-butylbenzylamine, 397 TFA, see Trifluoroacetic acid (TFA) Thalidomide, 48 Theory, NMR chemical shift, 98–99 nuclear resonance and relaxation, 96–98 nuclei magnetic properties, 94–96 spin coupling, 99–100 Thermally initiated polymerization, 246–247 Thermodynamic equilibrium, 12 Thiazoles, 117 Thiophilic structures, 5 Time-of-flight mass spectrometry (TOF-MS), 203 “Time slice,” 107 Time-space domain, 419 T-IR, see Transmission infrared (T-IR) mode TLD, see Trilinear decomposition (TLD) TOF-MS, see Time-of-flight mass spectrometry (TOF-MS) P-toluidine, 398 Total correlation spectroscopy (TOCSY), 114, 123 Toxicity, see ADMET behavior TP, see Tracer pulse (TP) method Trace analysis, 119–120, 122 Tracer pulse (TP) method, 424 Trailing electrolyte, 129 Transferring, 38 Transition energy levels, 95–96 Transmission infrared (T-IR) mode, 56 Transthyretin, 38 Triethylamine (TEA), 123 Trifluoroacetic acid (TFA), 101–102, 123 Trilinear decomposition (TLD), 203 Tripeptide libraries, 14 Two-dimensional DQCOSY, 118–119 Two-dimensional electrophoresis, 30 Two-dimensional peak capacity, 161 Two-dimensional separation applications, 157–158

van Deemter properties column diameter, 244 optimization, 170, 183 organic monolith columns, 238 reverse phase, 257 superficially porous particles, 287, 290 VCD, see Vibrational circular dichroism (VCD) Very low abundance proteins, 10–16 Vibrational circular dichroism (VCD) enantioselectivities, 85 fundamentals, 58–59 literature studies, 81 molecular simulations, 63 sorbent/solvent interactions, 71 Vibrational spectroscopies, 56–59 Volume of sample, 12

U Uniform magnetic susceptibility, 110 Unstable products, 125–127 Upstream processing, 48 Urine, see Human biologicals “Utilization distribution,” 161

W Wall effects, 241–243 Watershed algorithm, 199 Water suppression enhanced through T1 effects (WET) method, 113–115 WETTNTOCSY, 120 Whelk-01 chiral stationary phases, 431, 432 White wines, 15–16 Window target testing factor analysis (WTTFA), 206 Wraparound, absence, 154 WTTFA, see Window target testing factor analysis (WTTFA)

X X-ray diffraction (XRD) chiral discrimination, polysaccharide phases, 59 dry PS sorbents, 63 enantioselectivities, 74 PPA with three sorbents, 75, 77 XTerra columns, 325, 348

Z Zaramella, see Camurri and Zaramella instrument Zipax, 283 Zocor, 48 Zwittertonic properties anion exchangers, 3 polyprotic compounds, 407 sorbents, 3

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